MrHphysics
AP Physics 1: Motion
Enduring Understandings: Enduring Understanding 1.A: The internal structure of a system determines many properties of the system. Enduring Understanding 1.C: Objects and systems have properties of inertial mass and gravitational mass that are experimentally verified to be the same and that satisfy conservation principles. Enduring Understanding 2.B: A gravitational field is caused by an object with mass. Enduring Understanding 3.A: All forces share certain common characteristics when considered by observers in inertial reference frames. Enduring Understanding 4.A: The acceleration of the center of mass of a system is related to the net force exerted on the system, where: Fnet = mass * acceleration
Essential Knowledge: Essential Knowledge 3.A.1: An observer in a particular reference frame can describe the motion of an object using such quantities as position, displacement, distance, velocity, speed, and acceleration. Essential Knowledge 3.A.2: Forces are described by vectors. Essential Knowledge 3.A.3: A force exerted on an object is always due to the interaction of that object with another object. Essential Knowledge 4.A.1: The linear motion of a system can be described by the displacement, velocity, and acceleration of its center of mass. Essential Knowledge 4.A.2: The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time.
I kind of know what this is, but could not test well
I have a moderate grasp of this concept
I know what this is and could test well
I have a thorough understanding and could teach this to another
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(RATE YOUR UNDERSTANDING OF THE OBJECTIVES) *For signatures, if the student attempts to explain a concept to you, but not thoroughly and not to a point where you feel they understand it, initial NY for not yet. A NY will help a student identify areas of focus. Initial when they describe the concept well enough for you to understand it as well.
Learning Objective 3.A.1.1: The student is able to express the motion of an object using narrative, mathematical, and graphical representations [Science Practice 1.5, 2.1 and 2.2]
Learning Objective 3.A.1.2: The student is able to design an experimental investigation of the motion of an object. [Science Practice 4.2]
Learning Objective 3.A.1.3: The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. [Science Practice 5.1] Learning Objective 4.A.1.1: The student is able to use representations of the center of mass of an isolated two – object system to analyze the motion of the system qualitatively and semi-quantitatively. [Science Practice 1.2, 1.4, 2.3 and 6.4] Learning Objective 4.A.2.1: The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. [Science Practice 6.4] Learning Objective 4.A.2.3: The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [Science Practice 1.4 and 2.2] Learning Objective 4.A.2.2: The student is able to evaluate using given data whether all the forces on a system or whether all the parts of a system have been identified. [Science Practice 5.3]
SIGNATURES/Initials
I have no idea 1.
AP PHYSICS 1 CHART OF UNDERSTANDING UNIT: MOTION
MOTION PREVIEW Kinematics is the study of how things move – how far (distance and displacement), how fast (speed and velocity), and how fast that how fast changes (acceleration). We say that an object moving in a straight line is moving in one dimension, and an object which is moving in a curved path (like a projectile) is moving in two dimensions. We relate all these quantities with a set of equations called the kinematic equations. Vocabulary Terms: acceleration the rate of change in velocity acceleration due to gravity 2 the acceleration of a freely falling object in the absence of air resistance, which near the Earth’s surface is approximately 10 m/s . average velocity the velocity of an object measured over a time interval; the displacement of an object divided by the change in time during the motion constant (or uniform) velocity velocity which does not change during a time interval displacement change in position in a particular direction (vector) distance the length of a path (scalar) free fall motion under the influence of gravity inertial reference frame a frame of reference which is not accelerating. All Newtonian laws of forces and motion work within the frame initial velocity the velocity at which an object starts at the beginning of a time interval instantaneous the value of a quantity at a particular instant of time, such as instantaneous position, velocity, or acceleration kinematics the study of how motion occurs, including distance, displacement, speed, velocity, acceleration, and time. non-inertial reference frame A reference frame that is accelerated. Newton’s laws appear not to work within an accelerated frame unless compensation to the formulas are made to account for the acceleration of the frame. position-time graph the graph of the motion of an object that shows how its position varies with time scalar a quantity of magnitude such as speed or distance that is not dependent on direction speed the rate of distance travelled per unit time velocity vector quantity of displacement per unit time
Equations and Symbols
v
a
vo t
v
vo
at
x
(vo
v)t / 2
x
vot
1 2
v2
vo 2
at 2
2a x
Where: Δx = displacement (final position – initial position) v = velocity or speed at any time vo = initial velocity or speed t = time a = acceleration
Graphical Analysis of Motion Key Concept(s):
Example 1: In the following graph, determine: a) total displacement b) average velocity for the entire 10s
Example 2: In the following graph, determine: a) the time when the particle is at maximum velocity b) the time when the particle is at minimum velocity c) the time when the particle is at minimum speed d) the time when the particle is at maximum speed e) average velocity for the entire 8s
Example 3: The velocity of an object moving is graphed as shown in the figure. A) Determine the acceleration of the particle B) Determine total displacement from t = 0s to t = 9s
Example 4: The velocity of an object moving is graphed as shown in the figure. If x = 0.0m at t = 0s, A) What time is the particle at the greatest displacement from the origin? B) What is the acceleration of the particle at t = 6.0 s? C) What is the displacement for the first 4 seconds? D) During what time frames is acceleration zero?
Example 5 & 6: Sketch the corresponding velocity vs. time graph OR position vs. time graph for the given graph:
(additional practice/sketching)
Problem Solving for Motion in 1 Dimension Key Concept(s):
Example 1: A diver jumps off a 2.0m-high diving board and reaches the water 1.0 s later, 2.0m beyond the end of the board. Determine: a) Their initial velocity b) Maximum height reached c) Final velocity when they reach the water
Example 2: A ball thrown vertically upwards is caught by the thrower after 3.5 seconds at the same height from which it was thrown. a) Find the initial velocity of the ball. b) Find the maximum height reached by the ball.
Example 3: A car speeds up from 20m/s to 30m/s in 5 seconds. Then continues at that speed for 5 seconds. Determine the total displacement of the car for the entire 10 seconds.
Example 4: Two rocks are released from the top of a building and fall to the street below. One rock is dropped from rest and simultaneously the other rock is thrown downward at 20.0 m/s. It is observed that one rock hits the street 1.00 seconds before the other. Determine the height of the building.
Example 5: A speeding motorist travels at 30m/s while it passes a police car (at rest). If the police car begins chasing exactly when the car passes in front of him and accelerates at 6m/s2 A. When will she catch up to the motorist? B. How far down the road will they be when the cars paths intersect?
Problem Solving for Motion in 2 Dimensions Key Concept(s):
Example 1: A raft moves 5m/s perpendicular (across) a river, while the river drifts at 2m/s downstream. Determine the resultant velocity of the raft
Example 2: Blinky kicks a soccer ball 20m/s at 30o to the ground. Find both the horizontal and vertical components of velocity.
Example 3: Blinky is fired out of a cannon at 55m/s at a 45o angle. Find both horizontal and vertical components of his velocity immediately after leaving the cannon.
Projectile Motion Key Concept(s):
Conceptual Example: A water fountain has different streams of water coming out at the same velocity but different angles. Explain why the water streams have different peak heights and different ranges
Example 1: Derive an expression for horizontal range of a projectile that is launched and land from the same height in terms of the fundamental constants: v, g, Ө
Example 2: Derive an expression for maximum height of a projectile in terms of the fundamental constants: v, g, Ө
Example 2b: Express the maximum height (ymax) and range (Δx) with respect to each other with a formula.
Example 3: Derive an expression for time in the air of a projectile that is launched and land from the same height in terms of the fundamental constants: v, g, Ө
Example 4: For a projectile that is launched from the ground at 20m/s and 200 above horizontal, determine the velocity after 1 second. (be sure to include both magnitude and direction)
Textbook (Giancoli) Example 1: (II) Romeo is chucking pebbles gently up to Juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. 3–34). How fast are the pebbles going when they hit her window?
Textbook (Giancoli) Example 2: (II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m s at an angle of 37.0º with the horizontal, as shown in Fig. 3–35. (a) Determine the time taken by the projectile to hit point P at ground level. (b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find (c) the horizontal and the vertical components of its velocity, (d) the magnitude of the velocity, and (e) the angle made by the velocity vector with the horizontal. (f) Find the maximum height above the cliff top reached by the projectile.
Textbook (Giancoli) Example 3: (III) A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 250 km h 69.4 m s , (a) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. 3–37a)? (b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climbers’ position (Fig. 3–37b)? (c) With what speed do the supplies land in the latter case?
Inertial and Non-Inertial Reference Frames Key Concept(s):
Example 1: A student rides an elevator that is moving upwards at 1m/s. They drop a pencil in elevator and it falls from their hand to the elevator floor (1m from the hand to the elevator floor) From each perspective, determine the values: Perspective: Inside the elevator Outside the Elevator
A) Initial velocity B) Final velocity C) Acceleration
Example 2: In the case above, if the elevator cord snaps (putting the entire elevator in free-fall) 0.1 seconds after the student releases the pencil, describe the motion of the pencil from both perspectives Inside the elevator
Outside the Elevator
Example 3: A student is in a school bus which is moving at an initial velocity of 10m/s, in the process of braking (accelerates at 2.0m/s2). The student throws an orange directly upwards from his perspective. Sketch the trajectory of the orange from the perspectives of: Outside the bus
Inside the bus
College Board Released AP Motion Problems: (http://apcentral.collegeboard.com)
2014 APB
1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity the sprinter had after 2 seconds. a.
Determine the sprinter's constant acceleration during the first 2 seconds.
b.
Determine the sprinters velocity after 2 seconds have elapsed.
c.
Determine the total time needed to run the full 100 meters.
d.
On the axes provided below, draw the displacement vs time curve for the sprinter.
2006B2. A world-class runner can complete a 100 m dash in about 10 s. Past studies have shown that runners in such a race accelerate uniformly for a time t and then run at constant speed for the remainder of the race. A world-class runner is visiting your physics class. You are to develop a procedure that will allow you to determine the uniform acceleration a and an approximate value of t for the runner in a 100 m dash. By necessity your experiment will be done on a straight track and include your whole class of eleven students. (a) By checking the line next to each appropriate item in the list below, select the equipment, other than the runner and the track, that your class will need to do the experiment. Stopwatches
Tape measures
Metersticks
Starter's pistol
Rulers String
Masking tape Chalk
(b) Outline the procedure that you would use to determine a and t, including a labeled diagram of the experimental setup. Use symbols to identify carefully what measurements you would make and include in your procedure how you would use each piece of the equipment you checked in part (a). (c) Outline the process of data analysis, including how you will identify the portion of the race that has uniform acceleration, and how you would calculate the uniform acceleration.
1993B1 (modified) A student stands in an elevator and records his acceleration as a function of time. The data are shown in the graph above. At time t = 0, the elevator is at displacement x = 0 with velocity v = 0. Assume that the positive directions for displacement, velocity, and acceleration are upward. a. Determine the velocity v of the elevator at the end of each 5-second interval. i. Indicate your results by completing the following table. Time Interval (s)
0–5
5–10
10–15
15–20
v (m/s)
ii. Plot the velocity as a function of time on the following graph.
b.
Determine the displacement x of the elevator above the starting point at the end of each 5-second interval. i. Indicate your results by completing the following table. Time Interval (s)
0–5
5–10
10–15
15–20
x (m)
ii. Plot the displacement as a function of time on the following graph.
1994B1 (modified) A ball of mass 0.5 kilogram, initially at rest, is kicked directly toward a fence from a point 32 meters away, as shown above. The velocity of the ball as it leaves the kicker's foot is 20 meters per second at an angle of 37° above the horizontal. The top of the fence is 2.5 meters high. The ball hits nothing while in flight and air resistance is negligible. a.
Determine the time it takes for the ball to reach the plane of the fence.
b.
Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how far above the top of the fence will it pass?
c.
On the axes below, sketch the horizontal and vertical components of the velocity of the ball as functions of time until the ball reaches the plane of the fence.
2000B1 (modified) A 0.50 kg cart moves on a straight horizontal track. The graph of velocity v versus time t for the cart is given below.
a.
Indicate every time t for which the cart is at rest.
b.
Indicate every time interval for which the speed (magnitude of velocity) of the cart is increasing.
c.
Determine the horizontal position x of the cart at t = 9.0 s if the cart is located at x = 2.0 m at t = 0.
d.
On the axes below, sketch the acceleration a versus time t graph for the motion of the cart from t = 0 to t = 25 s.
e.
From t = 25 s until the cart reaches the end of the track, the cart continues with constant horizontal velocity. The cart leaves the end of the track and hits the floor, which is 0.40 m below the track. Neglecting air resistance, determine each of the following: i. The time from when the cart leaves the track until it first hits the floor ii. The horizontal distance from the end of the track to the point at which the cart first hits the floor
2002B1 (modified) A model rocket is launched vertically with an engine that is ignited at time t = 0, as shown above. The engine 2 provides an upward acceleration of 30 m/s for 2.0 s. Upon reaching its maximum height, the rocket deploys a parachute, and then descends vertically to the ground.
a.
Determine the speed of the rocket after the 2 s firing of the engine.
b.
What maximum height will the rocket reach?
c.
At what time after t = 0 will the maximum height be reached?
*1979M1 (modified) A ball of mass m is released from rest at a distance h above a frictionless plane inclined at an angle of 45° to the horizontal as shown above. The ball bounces horizontally off the plane at point P 1 with the same speed with which it struck the plane and strikes the plane again at point P 2. In terms of g and h determine each of the following quantities: a. The speed of the ball just after it first bounces off the plane at P1. b. The time the ball is in flight between points P1 and P2. c. The distance L along the plane from P1 to P2. d. The speed of the ball just before it strikes the plane at P2.
2005B1 (modified) The vertical position of an elevator as a function of time is shown above.
a. On the grid below, graph the velocity of the elevator as a function of time.
b.
i.
Calculate the average acceleration for the time period t = 8 s to t = 10 s.
ii.
On the box below that represents the elevator, draw a vector to represent the direction of this average acceleration.
2006Bb1. A student wishing to determine experimentally the acceleration g due to gravity has an apparatus that holds a small steel sphere above a recording plate, as shown above. When the sphere is released, a timer automatically begins recording the time of fall. The timer automatically stops when the sphere strikes the recording plate. The student measures the time of fall for different values of the distance D shown above and records the data in the table below. These data points are also plotted on the graph.
Distance of Fall (m)
0.10
0.50
1.00
1.70
2.00
Time of Fall (s)
0.14
0.32
0.46
0.59
0.63
(a) On the grid above, sketch the smooth curve that best represents the student's data
The student can use these data for distance D and time t to produce a second graph from which the acceleration g due to gravity can be determined. (b) If only the variables D and t are used, what quantities should the student graph in order to produce a linear relationship between the two quantities? (c) On the grid below, plot the data points for the quantities you have identified in part (b), and sketch the best straight-line fit to the points. Label your axes and show the scale that you have chosen for the graph.
(d) Using the slope of your graph in part (c), calculate the acceleration g due to gravity in this experiment. (e) State one way in which the student could improve the accuracy of the results if the experiment were to be performed again. Explain why this would improve the accuracy.
Multiple-Choice Questions (from njctl.org) PSI AP Physics 1 Kinematics Multiple-Choice Questions
1. An object moves around a circular path of radius R. The object starts from point A, goes to point B and describes an arc of half of the circle. Which of the following is true about the magnitude of displacement and traveled distance? Displacement Traveled Distance A. R 2R B. 2R πR C.
R
D.
R
4πR
2. A rock is thrown straight up from the edge of a cliff. The rock reaches the maximum height of 15 m above the edge and then falls down to the bottom of the cliff 35 m below the cliff. What is the traveled distance of the rock? A. 30 m B. 35 m C. 50 m D. 65 m 3. A rock is thrown straight up from the edge of a cliff. The rock reaches the maximum height of 15 m above the edge and then falls down to the bottom of the cliff 35 m below the cliff. What is the displacement of the rock? A. 15 m B. 35 m C. 50 m D. 65 m 4. Can an object’s average velocity equal zero when object’s speed is greater than zero? A. Yes, when the object moves in a straight line at a constant rate B. Yes, when the object returns to its original position C. No, it is impossible because they are always equal D. No, it is impossible because the magnitude of the velocity is always greater that speed 5. A car accelerates from rest at a constant rate 5 m/s2. Which of the following statements is true? A. The car travels 5 m in every second B. The car decreases its velocity 5 m/s in every second C. The car increases its velocity 5 m/s in every second D. The car’s velocity doesn’t change
An object is thrown straight up with an initial velocity v0. The graph represents the object’s vertical displacement as a function of time. Use the graph to the right for questions 6 through 8. 6. What is the total flying time of the object? A. 2 s B. 4 s C. 6 s
D. 8 s
7. At what time the object reaches its maximum height? A. 2 s B. 4 s C. 6 s D. 8 s 8. What is the initial velocity v0 of the object? A. 20 m/s B. 60 m/s C. 80 m/s
D. 50 m/s
9. Which of the following graphs represents the velocity as a function of time of an object thrown straight up?
A.
C.
B.
D.
10. Which of the following graphs represents the acceleration as a function of time of an object thrown straight up?
A.
B.
C.
D.
The relationship between the position and time of a moving object is shown on the graph. Use this graph for questions 11 and 12.
11. What is the instantaneous speed of the object at 4 s? A. 1 m/s B. 2 m/s C. 3 m/s D. 4 m/s 12. During which of the following times does the object accelerate? A. 0 s to 2 s B. 2 s to 4 s C. 0 s to 4 s D. 4 s to 8 s
The graph to the right describes the relationship between velocity and time for a moving object. Use this graph for questions 13 through 18. 13. What is the acceleration at time t = 1 s? A. 4 m/s2 B. 2 m/s2 C. -2 m/s2 D. -4 m/s2 14. What is the acceleration at time t = 8 s? A. 4 m/s2 B. -2 m/s2 C. -4 m/s2 D. 0 m/s2 15. What is the acceleration at time t = 6 s? A. 1 m/s2 B. 2 m/s2 C. -4 m/s2 D. 0 m/s2 16. What is the total displacement for the entire trip? A. 18 m B. 12 m C. 6 m D. 30 m 17. What is the total traveled distance for the entire trip? A. 18 m B. 12 m C. 6 m D. 30 m 18. Between what times does the object approach the origin at the constant speed? A. 2 s to 5 s B. 6 s to 7 s C. 7 s to 9 s D. 9 s to 10 s 19. A rock is thrown straight up with twice the initial velocity of another. How much higher will the first rock be at its apex? A. 2 times B. 4 times C. 16 times D. The rocks will reach the same apex point 20. A student drops a pebble from the edge of a vertical cliff. The pebble hits the ground 4 s after it was dropped. What is the speed of the pebble just before it hits the ground? A. 20 m/s B. 40 m/s C. 60 m/s D. 80 m/s 21. A student drops a pebble from the edge of a vertical cliff. The pebble hits the ground 4 s after it was dropped. What is the height of the cliff? A. 20 m B. 40 m C. 60 m D. 80 m 22. An Astronaut on the Moon simultaneously drops a bird feather and a screw driver. The fact that two objects reach the surface at the same time can be explained by which of the following? A. The Moon has no gravity B. The Moon’s gravity is much weaker than the Earth’s gravity C. The same gravitational force is applied on both objects on the Moon D. At the given location all objects fall with the same acceleration in the absence of air resistance
23. A marble launcher shoots a marble horizontally from the height of 0.2 m above a horizontal floor. The marble lands on the floor 5 m away from the launcher. How long did the marble stay in are? A. 0.1 s B. 0.2 s C. 0.3 s D. 0.4 s 24. A marble launcher shoots a marble horizontally from the height of 0.2 m above a horizontal floor. The marble lands on the floor 5 m away from the launcher. What is the initial speed of the marble? A. 5 m/s B. 10 m/s C. 15 m/s D. 25 m/s
25. A bicyclist moves a long a straight line with an initial velocity v0 and slows down. Which of the following the best describes the signs set for the initial position, initial velocity and the acceleration? Initial position Initial velocity Acceleration A. Positive Positive Negative B. Negative Positive Negative C. Negative Negative Positive D. Negative Negative Negative 26. Which of the following is a vector quantity? A. Traveled distance B. Displacement
C. Area
27. Which of the following is not a vector quantity? A. Velocity B. Displacement C. Momentum
A vector of displacement D is placed in X-Y coordinate system shown in the diagram to the right. Use this diagram to answer questions 28 through 30. 28. What is the x-component of vector D? A. 2 m B. 3 m C. 4 m
D. 5 m
29. What is the y-component of vector D? A. 2 m B. 3 m C. 4 m
D. 5 m
30. What is the magnitude of vector D? A. 2 m B. 3 m C. 4 m
D. 5 m
D. Mass
D. Traveled distance
31. An object changes its velocity from V1 to V2 during a time interval Δt. Which of the following is the correct direction for the object’s acceleration?
A.
C.
B.
D.
32. A projec le is fired at above the horizontal line with an initial velocity v0. At which of the following angles the projectile will land at the same distance as it is landed in the first trial? A. 2 B. 3 C. 4 D. 4
33. When a projectile reaches the highest point the vertical component of the acceleration is:
A. Greater than g
B. Positive g
C. Negative g
D. Zero
34. When a projectile reaches the highest point the horizontal component of the acceleration is: A. Less than g B. Positive g C. Negative g D. Zero 35. An object is thrown in horizontal with an initial velocity v0= 5 m/s from the roof of a building 40 m tall. How much later does it hit the ground? A. 4 s
B.
s
C.
s
D. 10 s
36. An object is thrown in horizontal with an initial velocity v0= 10 m/s from the roof of a building 20 m tall. How far from the building does it hit the ground? A. 5 m B. 10 m C. 15 m D. 20 m
The diagram to the right represents a swimmer. The swimmer is capable to swim in a still water with a velocity V1 = 1 m/s. He aims his body directly across a 100 m wide river whose current has a velocity V2 = 2 m/s. Use this diagram to answer questions 37 through 39. 37. How much time it will take for the swimmer to cross the river? A. 10 s B. 20 s C. 50 s D. 100 s 38. How far downstream will he land? A. 100 m B. 200 m
C. 150 m
D. 180 m
39. What is the velocity of the swimmer relative to the river bank? A. 1 m/s
B. 2 m/s
C.
m/s
D. m/s
40. The graphs above represent the position, velocity, and acceleration as a function of time for a marble moving in one dimension. Which of the following could describe the motion of the marble? A. Rolling along the floor and then bouncing off a wall. B. Rolling down one side of a bowl and then rolling up the other side. C. Rolling up a ramp and then rolling back down. D. Falling and then bouncing elastically off a hard floor.
Multi-Correct Questions 41. Position as a function of time of a moving object is presented by the graph. Which of the following is true about the type of motion? A. The object moves with a constant positive acceleration B. The object moves with a constant positive velocity C. The slope of this graph is equal to the object’s acceleration D. The slope of this graph is equal to the object’s velocity
42. Position as a function of time of two moving objects is presented by the graph. Which of the following statements is true? A. Object I has a greater velocity than object II B. Object II has a greater velocity that object I C. At time t0 they have the same velocity D. At time t0 object II passes by object I
43. A projectile is fired from the ground level with an initial velocity v0. Which of the following statements is true? A. Vertical component of the velocity at point C is v0 sinθ B. Horizontal component of the velocity at point C is v0 cosθ C. The projectile travels with the same speed at point B and D D. The acceleration at point C is zero
44. An object accelerates from rest at a constant rate. Which of the following graphs could be used to describe the motion of the object?
A.
C.
B.
D.
45. A tennis ball is thrown straight up and caught at the same height. Which of the following can describe the motion of the ball when it reaches the apex? A. The velocity of the ball is zero. B. The acceleration of the ball is zero. C. The acceleration of the ball is 9.8 m/s2 down D. The acceleration of the ball is 9.8 m/s2 up.
Free Response Problems 1. A car whose speed is 20 m/s passes a stationary motorcycle which immediately gives chase with a constant acceleration of 2.4 m/s2. a. How far will the motorcycle travel before catching the car? b.How fast will it be going at that time? c. How does that compare to the car’s velocity? d.Draw the following graphs for the car: x(t), v(t), a(t). e. Draw the following graphs for the motorcycle: x(t), v(t), a(t). f. Write the equation of motion for the car. g. Write the equation of motion for the motorcycle.
2. A lab cart moves a long a straight horizontal track. The graph describes the relationship between the velocity and time of the cart. a. Indicate every time interval for which speed (magnitude of the velocity) of the cart is decreasing. b. Indicate every time at which the cart is at rest. c. Determine the horizontal position x of the cart at t = 4 s if the cart is located at x0 = when t0 = 0. d.Determine the traveled distance of the cart over 10 s from the beginning. e.Determine the average speed of the cart for this time interval. f. Find the acceleration of the cart during time: 0 s -4 s, 4 s – 8 s, 8 s – 10 s, 10 s – 14 s, 14 s – 16 s, 16 s – 20 s. g. On the axes below, sketch the acceleration graph for the motion of the cart from t = 0 s to t = 20 s.
3. Find the magnitude and the direction of vector C for the following cases. a.A at , B = 20 N at , C = A + B b.A at , B = 20 N at ,C=A+B c. A at , B = 20 N at ,C=A+B d.A at , B = 20 N at , C = A + B e.A at , B = 20 N at , C = A + B 4. Find the magnitude and the direction of vector G as a sum of two vectors D and E by going through the following steps. a.D at 3 . Find Dx and Dy. b. E 2 at 2 . Find Ex and Ey. c. Find Gx = Dx + Ex d.Find Gy = Dy + Ey e. Find the magnitude of G from its components f. Find the direction of G. 5. Find the magnitude and the direction of vector C for the following cases. a.A 4 at , B = 10 N at , C = A + B b.A 4 at , B = 10 N at ,C=A+ B c. A 4 at , B = 10 N at ,C =A+B d.A 4 at , B = 10 N at , C = A + B e.A 4 at , B = 10 N at , C = A + B 6. Find the magnitude and the direction of vector G as a sum of two vectors D and E by going through the following steps. a.D 3 at . Find Dx and Dy. b. E 4 at . Find Ex and Ey. c. Find Gx = Dx + Ex d.Find Gy = Dy + Ey e. Find the magnitude of G from its components f. Find the direction of G. 7. Two forces 3 at and 4 at pull on an object. Answer the following: a. Draw a diagram showing the forces acting on the object. b.Draw a sketch showing the vector sum of two forces. c. Find the magnitude of the resultant force. d.Find the direction of the resultant force.
8. A ship makes three displacements in the following order: 1) mi 4 north of east 2) 50 mi, 56 north of west; and 3) 47 mi, south a. Draw a clear diagram showing all three displacement vectors with respect to horizontal points (north, east, south, and west). b. Find the X and Y components of displacement D1. c. Find the X and Y components of displacement D2. d.Find the X and Y components of displacement D3. e.Find the magnitude of the resultant vector. f. Find the direction of the resultant vector. 9. A bus makes three displacements I the following order: 4) mi 3 east of north 5) mi 4 west of north; and 6) 75 mi, south-east a. Draw a clear diagram showing all three displacement vectors with respect to horizontal points (north, east, south, and west). b. Find the X and Y components of displacement D1. c. Find the X and Y components of displacement D2. d.Find the X and Y components of displacement D3. e.Find the magnitude of the resultant vector. f. Find the direction of the resultant vector. 10. A ball is thrown horizontally from the roof of a building 75 m tall with a speed of 4.6 m/s. a. How much later does the ball hit the ground? b.How far from the building will it land? c. What is the velocity of the ball just before it hits the ground? 11. A projec le is fired with an ini al speed of m s at an angle of 4 above the horizontal. a. Determine the total time in the air. b. Determine the maximum height reached by the projectile. c. Determine the maximum horizontal distance covered by the projectile. d.Determine the velocity of the projectile 5 s after firing. 12. A projec le is fired from the edge of a cli m high with an ini al speed of m s at an angle of 3 above the horizontal. a. Determine the total time in the air. b. Determine the maximum height reached by the projectile. c. Determine the maximum horizontal distance covered by the projectile. d.Determine the velocity of the projectile just before it hits the bottom of the cliff.
13. A ball is thrown horizontally from the roof of a building 55 m tall with a speed of 3.8 m/s. a. How much later does it hit the ground? b. How far from the building will it land? c. What is the velocity of the ball just before it hits the ground? 14. A projectile is fired with an initial speed of 110 m/s at an angle of 36 above the horizontal. a. Determine the total time in the air. b. Determine the maximum height reached by the projectile. c. Determine the total horizontal distance covered by the projectile. d. Determine the velocity of the projectile 4s after firing. 15. A ball rolls off a 1.5 m tall horizontal table and lands on the floor .70 m away. a. How much time is the ball in the air? b. How does that time compare with the time it takes for a dropped ball to fall that same distance. c. What is the ball’s velocity while it was on the table top? d. What is the horizontal component of its velocity just prior to impact? e. What is the vertical component of its velocity just prior to impact? f. What is the magnitude of its velocity just prior to impact? g. What is the direction of its velocity just prior to impact? 16. An archer fires an arrow with a velocity of 42 m/s at an angle of 35 degrees above horizontal? a. What is the horizontal component of its initial velocity? b. What is the vertical component of its initial velocity? c. What is the maximum height attained by the arrow? d. How long does it take the arrow to reach that height? e. What is the total amount of time that it’s in the air? f. How far away does it strike the ground? g. What is the horizontal component of its velocity just prior to impact? h. What is the vertical component of its velocity just prior to impact? i. What is the magnitude of its velocity just prior to impact? j. What is the direction of its velocity just prior to impact? 17. A cannon is fired horizontally from a cliff 112m high with a speed of 25 m/s. a. How much later does the cannon ball hit the ground? b. How far from the cliff will it land? c. What is the velocity of the cannon ball just before it hits the ground? 18. A ball is thrown horizontally from the roof of a building 12 m tall with a speed of 3.1 m/s. a. How much later does the ball hit the ground? b. How far from the building will it land? c. What is the velocity of the ball just before it hits the ground?
19. A gazelle leaps from a cliff 2.5 m high with a speed of 5.6 m/s. a. How much later does the gazelle hit the ground? b. How far from the cliff will it land? c. What is the velocity of the gazelle just before it hits the ground? 20. A projectile is fired with an initial speed of 40 m/s at an angle of 23 degrees above the horizontal. a. Determine the total time in the air. b. Determine the maximum height reached by the projectile. c. Determine the maximum horizontal distance covered by the projectile. d. Determine the velocity of the projectile 2s after firing. 21. A hose held near the ground shoots water at a speed of 3.5 m/s at an angle of 72 degrees above the horizontal. a. Determine the total time of the water in the air. b. Determine the maximum height reached by the water. c. Determine the maximum horizontal distance covered by the water. 22. You are riding your bike at 10 m/s when you see your friend 20 m in front of you. You apply the brakes and slow down with a rate of 2.5 m/s2. a. Write and equation that can describe your position at a function of time. b. Write and equation that can describe your velocity as a function of time. c. On the graphs below sketch the velocity vs. time and position vs. time graphs.
d. How long will it take you to come to a complete stop? Justify your answer. e. Will you come to a stop before you get to your friend, exactly where your friend is standing, or after you pass your friend? Justify your answer.
Answers Multiple Choice 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.
C D B B C D B B C B B D B D C C D C B B D D B D C B D B C D B B C D C D D B 36 https://sites.google.com/site/mrhphysics/
39. 40. 41. 42. 43. 44. 45.
D B B&D B&D B&C B&D A&C
Free Response 1. a. 333 m b. 40 m/s c. twice the speed
d.
e. f. g. 2. a. 8 to 10 s b. 10 to 14 s c. 8 m d. 28 m e. 2.8 m/s f. 1 m/s2, 0, -2 m/s2, 0, -1 m/s2, 0
g. 3. a. 30N at 0o b. 10N at 180o c. 30N at 180o d. 22.4N at 63o e. 22.4 at 26.6o 4. a. 8.0 N and 6.0 N b. 18.1 N and 8.5 N c. 26.1 N 37 https://sites.google.com/site/mrhphysics/
d. 12.7 N e. 29 N f. 25.9 o 5. a. 50 N at 0o b. 30 N at 0o c. 50 N at 180o d. 41.2 N at 14o e. 41.2 N at 76o 6. a. 12.7 N and 27.2 N b. 43.5 N and 11.6 N c. 56.2 N d. 38.8 N e. 68.3 N f. 34.6o
7. a.
b. c. 500 N d. 53.1o
8. a. b. 50.9 mi and 56.5 mi c. -27.9 mi and 41.5 mi d. 0 mi and -47 mi e. 55.9 mi f. 65.7o North of East
9. a. 38 https://sites.google.com/site/mrhphysics/
b. 35.7 mi and 45.7 mi c. -49.6 mi and 47.9 mi d. 53.0 mi and -53.0 mi e. 56.4 mi f. 46.1o 10. a. 3.9 s b. 18 m c. 39.3 m/s at 305 o 11. a. 2 s b. 614 o c. 2244 m d. 118 m
12. a. 8.4 s b. 14 m c. 335.2 m/s d. 65.7 m/s at 54 o 13. a. 3.4 s b. 12.7 m c. 33 m/s 14. a. 13.3 s b. 215.6 m c. 1184 m d. 92.4 m/s 15° above horizontal 15. a. 0.38 s b. The time is the same. c. 3.9 m/s d. 3.9 m/s e. 3.7 m/s f. 5.4 m/s g. 44° below horizontal 16. a. 34 m/s b. 24 m/s c. 29.4 m d. 2.4 s e. 4.8 s f. 13.2 m 39 https://sites.google.com/site/mrhphysics/
g. 34 m/s h. -24 m/s i. 42 m/s j. 35° below horizontal 17. a. 4.8 s b. 119.5 m c. 53 m/s 61° below horizontal 18. a. 1.56 s b. 4.85 m c. 15.6 m/s 79° below horizontal 19. a. 0.7 s b. 4 m c. 8.9 m/s 50° below horizontal
20. a. 3.2 s b. 11.5 m c. 118 m d. 37.2 m/s 6° below horizontal 21. a. 3.3 m/s b. 0.68 s c. 0.56 m 22. a. b. c.
t
d. 4s e. Exactly where your friend is standing.
40 https://sites.google.com/site/mrhphysics/
41 https://sites.google.com/site/mrhphysics/
