1 KINEMATICS 1 - DISPLACEMENT & AVERAGE VELOCITY

1. After a tennis match, the players dash to the net to congratulate one another. If they both run with a speed of 3m/s, are their velocities equal?

2. A mass initially at O moves 10 m to the right and then 2 m to the left. What is the final displacement of the mass?

3. A mass initially at O, first moves 5 m to the right and then 12 m to the left. What is the total distance covered by the mass and what is its displacement?

4. An object has a displacement of —5 m. It moves a distance to the right equal to 15 m and then a distance of 10 m to the left. What is the total distance travelled and final displacement of the object?

5. A car starts out from O in a straight line and moves a distance of 20 km towards the right, and then returns to its starting position 1 h later. What is the average speed and the average velocity for this trip?

6. A motor car travels on a circular track of radius a, as shown in the figure. When the car has travelled from P to Q its displacement from P is A. a√2 southwest. B. a√2 northeast. C. 3πa/2 southwest. D. 3πa/2 northeast.

7. Juan is standing on the platform at a railway station. A train passes through the station with speed 20 ms-1 in the direction shown measured relative to the platform. Carmen is walking along one of the carriages of the train with a speed of 2.0 ms-1 measured relative to the carriage in the direction shown. Velocity is measured as positive in the direction shown on the diagram. The velocity of Carmen relative to Juan is A. -22 ms-1. B. -18 ms-1. C. +18 ms-1. D. +22 ms-1.

2 8. Four cars W, X, Y and Z are on a straight road. The graph below shows the variation with time t of the distance s of each car from a fixed point. Which car has the greatest speed? A. W B. X C. Y D. Z

9. An object is moving along a straight line. The graph shows the object's position from the starting point as a function of time. a. In which segment(s) of the graph does the object's average velocity (measured from t = 0 s) decrease with time? b. What was the instantaneous velocity of the object at t = 4 s? c. In which segments(s) of the graph does the object have the highest speed? d. At which time (s) does the object reverse its direction of motion?

10. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this week. She must get from one side of the school to the other by hurrying down three different hallways. She runs down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she covers its 48.0-m length at an average speed of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0-m length at a speed of 5.00 m/s. a) Does Suzette make it to class on time or does she get detention for being late again? b) Draw a distance vs. time graph of the situation.

3 11. An object is moving along a straight line in the positive x direction. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D. a. Which segment(s) of the graph represent(s) a constant velocity of +1.0 m/s? b. What was the instantaneous velocity of the object at the end of the eighth second? c. During which interval(s) did the object move in the negative x direction?

12. A pronghorn antelope has been observed to run with a top speed of 97 km/h. Suppose she runs 1.5 km with an average speed of 85 km/h, and then runs 0.80 km with an average speed of 67 km/h. a. How long will it take (in seconds) the antelope to run the entire 2.3 km? b. What is the antelope’s average speed during this time?

13. A particle travels along a curved path between two points P and Q as shown. The displacement of the particle does not depend on a. the location of P. b. the location of Q. c. the distance traveled from P to Q. d. the shortest distance between P and Q. e. the direction of Q from P. 14. For which one of the following situations will the path length equal the magnitude of the displacement? a. A jogger is running around a circular path. b. A ball is rolling down an inclined plane. c. A train travels 5 miles east; and then, it stops and travels 2 miles west. d. A ball rises and falls after being thrown straight up from the earth's surface. e. A ball on the end of a string is moving in a vertical circle.

15. A particle moves along the x axis from xi to xf . Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude? a. xi = 4m, xf = 6m c. xi = –4m, xf = 2m e. xi = –4m, xf = 4m b. xi = –4m, xf = –8m d. xi = 4m, xf = –2m

4 16. A particle moves along the x axis from xi to xf . Of the following values of the initial and final coordiantes, which results in a negative displacement? a. xi = 4m, xf = 6m d. xi = –4m, xf = –2m b. xi = –4m, xf = –8m e. xi = –4m, xf = 4m c. xi = –4m, xf = 2m

17. A particle moves along the x axis from xi to xf . Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude? a. xi = 4m, xf = 6m c. xi = –4m, xf = 2m e. xi = –4m, xf = 4m b. xi = –4m, xf = –8m d. xi = 4m, xf = –2m

18. A hiker travels south along a straight path for 1.5 h with an average velocity of 0.75 km/h, then travels south for 2.5 h with an average velocity of 0.90 km/h. What is the hiker’s displacement for the total trip? a. 1.1 km to the south b. 2.2 km to the south c. 3.4 km to the south d. 6.7 km to the south

19. a. The graph shows displacement versus time. What is the average velocity for line A? b. The graph above shows displacement versus time. What is the average velocity for line B? c. The graph above shows displacement versus time. What is the average velocity for line C?

5 HW2 – acceleration and graphs

1. Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her. Grace slams on the brakes and comes to a

stop in 3.0 s. What was the acceleration of Grace’s car?

2. Vivian is walking to the hairdresser’s at 1.3 m/s when she glances at her watch and realizes that she is going to be late for her appointment. Vivian gradually quickens her pace at a rate of 0.090 m/s2. a) What is Vivian’s speed after 10.0 s? b) At this speed, is Vivian walking, jogging, or running very fast?

3. A torpedo fired from a submerged submarine is propelled through the water with a speed of 20.00 m/s and explodes upon impact with a target 2000.0 m away. If the sound of the impact is heard 101.4 s after the torpedo was fired, what is the speed of sound in water? (Because the torpedo is held at a constant speed by its propeller, the effect of water resistance can be neglected.)

4. When velocity is positive and acceleration is negative, what happens to the object’s motion? a. The object slows down. c. Nothing happens to the object. b. The object speeds up. d. The object remains at rest.

5. In which one of the following situations does the car have a westward acceleration? a. The car travels westward at constant speed. b. The car travels eastward and speeds up. c. The car travels westward and slows down. d. The car travels eastward and slows down. e. The car starts from rest and moves toward the east.

6. Of the following situations, which one is impossible? a. A body having velocity east and acceleration east b. A body having velocity east and acceleration west c. A body having zero velocity and non-zero acceleration d. A body having constant acceleration and variable velocity e. A body having constant velocity and variable acceleration

7. In which one of the following cases is the displacement of the object directly proportional to the time? a. a ball rolls with constant velocity b. a ball at rest is given a constant acceleration c. a ball rolling with velocity vo is given a constant acceleration d. a bead falling through oil experiences a decreasing acceleration e. a rocket fired from the earth's surface experiences an increasing acceleration

8. Starting from rest, a particle confined to move along a straight line is accelerated at a rate of 5.0 m/s2. Which one of the following statements accurately describes the motion of this particle? a. The particle travels 5.0 m during each second. b. The particle travels 5.0 m only during the first second. c. The speed of the particle increases by 5.0 m/s during each second. d. The acceleration of the particle increases by 5.0 m/s2 during each second. e. The final speed of the particle will be proportional to the distance that the particle covers.

8a. Starting from rest, a particle which is confined to move along a straight line is accelerated at a rate of 5.0 m/s2. Which statement concerning the slope of the position versus time graph for this particle is true? a. The slope has a constant value of 5.0 m/s. b. The slope has a constant value of 5.0 m/s2. c. The slope is both constant and negative. d. The slope is not constant and increases with increasing time. e. The slope is not constant and decreases with increasing time.

9. Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

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10. A car accelerates from rest on a straight road. A short time later, the car decelerates to a stop and then returns to its original position in a similar manner. Which of the five following graphs best describes the motion?

11. The graph represents the straight line motion of a car. How far does the car travel between t = 2 seconds and t = 5 seconds?

a. 4 m b. 12 m c. 24 m d. 36 m e. 60 m

12. An object moving in a straight line according to the velocity - time graph has an initial displacement of 8.00 m. (a) What is the displacement after 8.00 s? (b) What is the displacement after 12.0 s? (c) What is the average speed and average velocity for this motion?

13. Find the displacement - time graph for an object moving in a straight line according to the velocity - time graph. The displacement is initially zero. You do not have to put any numbers on the axes.

14. A mass has an initial velocity of 10.0 m/s. It moves with acceleration - 2.00 m/s2 . When will it have zero velocity?

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15. What is the displacement after 10.0 s of a mass whose initial velocity is 2.00 m/s and moves with acceleration a = 4.00 m/s2 ?

16. A car has an initial velocity of 5.0 m/s . When its displacement increases by 20.0 m, its velocity becomes 7.0 m/s. What is the acceleration?

17. A body has initial velocity of 4.0 m/s and a velocity of v = 12 m/s after 6.0 s. What displacement did the body cover in the 6.0 s?

18. The car accelerate from rest to 28 m/s in 9.0 s. What distance does it travel?

19. A body has initial velocity of 12 m/s and is brought to rest over a distance of 45 m. What is the acceleration of the body?

20. What deceleration does a passenger of a car experience if his car, which is moving at 100.0 km/h, hits a wall and is brought to rest in 0.1000 s? Express the answer in m/s2 .

21. A car is travelling at 40.0 m/s. The driver sees an emergency ahead and 0.50 s later slams on the brakes. The acceleration of the car is - 4 m/s2. (a) What distance will the car travel before it stops? (b) If the driver was able to apply the brakes instantaneously without a reaction time, over what distance would the car stop? (c) Calculate the differnce in your answer to (a) and (b). (d) Assume now that the car was travelling at 30.0 m/s instead. Without performing any calculations, would the answer to (c) now be less than, equal to or larger than before? Explain your answer.

22. Figure shows the displacement versus time of an object moving in a straight line. Four points on this graph have been selected. (a) Is the velocity between A and B positive, zero or negative?

8 (b) What can you say about the velocity between B and C? (c) Is the acceleration between A and B positive, zero or negative? (d) Is the acceleration between C and D positive, zero or negative?

23. Find acceleration of the object at time t = 6 s. Sketch graph acceleration versus time for the object.

24. Figure shows the variation of the displacement of a moving object with time. Draw the graph showing the variation of the velocity of the object with time.

25. The figure shows the variation of the displacement of a moving object with time. Draw the graph showing the variation of the velocity of the object with time.

26. The figure shows the variation of the displacement of a moving object with time. Draw the graph showing the variation of the velocity of the object with time.

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27. The figure shows the variation of the displacement of a moving object with time. Draw the graph showing the variation of the velocity of the object with time.

28. The figure shows the variation of the displacement of a moving object with time. Draw the graph showing the variation of the velocity of the object with time.

29. The figure shows the variation of the velocity of a moving object with time. Draw the graph showing the variation of the displacement of the object with time.

30. The figure shows the variation of the velocity of a moving object with time. Draw the graph showing the variation of the displacement of the object with time.

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31. The figure shows the variation of the velocity of a moving object with time. Draw the graph showing the variation of the displacement of the object with time (assuming a zero initial displacement)

32. The figure shows the variation of the velocity of a moving object with time. Draw the graph showing the variation of the acceleration of the object with time.

11 KINEMATICS - DISPLACEMENT & AVERAGE VELOCITY Answer Section

1. Their velocities are different because they travel in different directions

2. 8 m to the right.

3. Total distance is 17 m. Displacement = - 7m to the left

4. Total distance is 25 m. Displacement = 0 m

5. The total distance covered is 40 km. average speed v = 40/1 = 40 km/h. Displacement = 0 m. Average velocity v = displacement/time = 0 km/h

6.A 7.B 8.A

9. a. BC and DE b. +10 m/s c. DE d. 5 s 10. a) First hallway: t = d/v = (35.0 m)/(3.50 m/s) = 10.0 s b. Second hallway: t = d/v = (48.0 m)/(1.20 m/s) = 40.0 s Third hallway: t = d/v = (60.0 m)/(5.00 m/s) = 12.0 s total time: 10.0 s + 40.0 s + 12.0 s = 62.0 s This is 2 s after the bell rings, so Suzette is late.

11. a. D b. 0 m/s c. only during interval C

12. ∆x1 = 1.5 km v1 = 97 km/h ∆x2 = 0.80 km v2 = 67 km/h

∆x = ∆x1 + ∆x2 = 2.3 km ∆t = ?

a. ∆t = ∆t1 + ∆t2 = 2.3 km

∆t = 64 s + 43 s = 107 s

b.

13. C 14. B 15. E 16.B 17. E 18. C

19. a. 3.0 m/s b. 1.0 m/s c. 0.3 m/s

12 HW - FREE FALL - HONORS

1. A ball is thrown upwards with a speed of 24 m/s. Take the acceleration due to gravity to be 10 m/s2.

(a) When is the velocity of the ball 12.0 m/s ? (b) When is the velocity of the ball - 12.0 m/s? (c) What is the displacement of the ball at those times? (d) What is the velocity of the ball 1.50 s after launch? (e) What is the maximum height reached by the ball?

2. A stone is thrown vertically upwards with an initial speed of 10.0 m/s2 from a cliff that is 50.0 m high. (a) When does it reach the bottom of the cliff? (b) What speed does it have just before hitting the ground? (c) What is the total distance traveled by the stone? Take the acceleration due to gravity to be 10 m/s2.

3. A rock is thrown vertically down from the roof of 25.0 m high building with a speed of 5.0 m/s. (a) When does the rock hit the ground? (b) With what speed does it hit the ground? Take the acceleration due to gravity to be 10 m/s2.

4. A window is 1.50 m high. A stone falling from above passes the top of the window with a speed of 3.00 m/s. When will it pass the bottom of the window? (Take the acceleration due to gravity to be 10 m/s2.)

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5. A ball is dropped from rest from a height of 20.0 m. One second later a second ball is thrown vertically downwards. If two balls arive at the ground at the same time, what must have been initial velocity of the second ball? (Take the acceleration due to gravity to be 10 m/s2.)

6. * A ball is dropped from rest from the top of a 40.0 m building. A second ball is thrown downward 1.0 s later. (a) If they hit the ground at the same time, find the speed with which the second ball was thown. (b) What is the ratio of the speed of the thrown ball to the speed of the other as they hit the ground? (Take the acceleration due to gravity to be 10 m/s2.)

7. * Two balls are dropped from rest from the same height. One of the balls is dropped 1.00 s after the other. What distance separates the two balls 2.00 s after the second ball is dropped? (Take the acceleration due to gravity to be 10 m/s2.)

8. * A mass is thrown upwards with an initial velocity of 30 m/s. A second mass is dropped from directly above, a height of 60 m from the first mass, 0.5 s later. When do the masses meet and how high is the point where they meet?

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9. * A hot air balloon is rising vertically at constant speed 5.0 m/s. A sandbag is released and it hits the ground 12.0 s later. (a) With what speed does the sandbag hit the ground? (b) How high was the balloon when the sandbag was released? (c) What is relative velocity of the sandbag with respect to the balloon 6.0 s after it was dropped? Assume that the balloon's velocity increased to 5.5 m/s after releasing sandbag. Take the acceleration due to gravity to be 10 m/s2.

10. An object with initial velocity 20 m/s and initial displacement - 75 m experiences an acceleration of - 2 m/s2 . Draw the displacement - time graph for this motion for the first 20 s.

11. An object moves in a straight line with an acceleration that varies with time as shown:

Initially the velocity of the object is 2.00 m/s. (a) Find the maximum velocity reached in the first 6.00 s of this motion. (b) Draw a graph of the velocity versus time.

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12. A stone is thrown vertically up from the edge of a cliff 35.0 m from the ground. The initial velocity of the stone is 8.00 m/s (a) How high will the stone get? (b) When will it hit the ground? (c) What velocity will it have just before hitting the ground? (d) What distance will the stone have covered? (e) What is the average speed and average velocity fro this motion? (f) Make a graph to show the variation of displacement with time. (g) Make a graph to show the variation of velocity with time. Take the acceleration due to gravity to be 10 m/s2.

13. A ball is thrown upward from the edge of a cliff with velocity 20.0 m/s. It reaches the bottom of the cliff 6.0 s later. (a) How hight is the cliff? (b) With what speed does the ball hit the ground?

14. A rocket accelerates vertically upwards from rest with a constant acceleration of 4.00 m/s2 . The fuel lasts for 5.00 s. (a) What is the maximum height achieved by this rocket? (b) When does the rocket reach the ground again? (c) Sketch a graph to show the variation of the velocity of the rocket with time from the time of launch to the time it falls to the ground. Take the acceleration due to gravity to be 10 m/s2.

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15. The baseball catcher throws a ball vertically upward and catches it in the same spot as it returns to the mitt. At what point in the ball’s path does it experience zero velocity and nonzero acceleration at the same time? a. midway on the way up b. at the top of its trajectory c. the instant it leaves the catcher’s hand d. the instant before it arrives in the catcher’s mitt

16. Ball A is dropped from rest from a window. At the same instant, ball B is thrown downward; and ball C is thrown upward from the same window. Which statement concerning the balls is necessarily true if air resistance is neglected? a. At some instant after it is thrown, the acceleration of ball C is zero. b. All three balls strike the ground at the same time. c. All three balls have the same velocity at any instant. d. All three balls have the same acceleration at any instant. e. All three balls reach the ground with the same velocity.

17. A rock is thrown vertically upward from the surface of the earth. The rock rises to some maximum height and falls back toward the surface of the earth. Which one of the following statements concerning this situation is true if air resistance is neglected? a. As the ball rises, its acceleration vector points upward. b. The ball is a freely falling body for the duration of its flight. c. The acceleration of the ball is zero when the ball is at its highest point. d. The speed of the ball is negative while the ball falls back toward the earth. e. The velocity and acceleration of the ball always point in the same direction.

18. A ball is in free fall. Its acceleration is: a. downward during both ascent and descent b. downward during ascent and upward during descent c. upward during ascent and downward during descent d. upward during both ascent and descent e. downward at all times except at the very top, when it is zero

19. A ball is in free fall. Upward is taken to be the positive direction. The displacement of the ball is: a. positive during both ascent and descent b. negative during both ascent and descent c. negative during ascent and positive during descent d. positive during ascent and negative during descent e. none of the above

20. A baseball is thrown vertically into the air. The acceleration of the ball at its highest point is: a. 9.8 m/s2 down b. 9.8 m/s2 up c. changing suddenly from 9.8 m/s2 up to 9.8 m/s2 down d. zero e. cannot be calculated without knowing the initial velocity

21. Which one of the following statements is correct for an object released from rest? a. The average velocity during the first second of time is 4.9 m/s b. During each second the object falls 9.8 m c. The acceleration changes by 9.8 m/s every second d. The object falls 9.8 m during the first second of time e. The acceleration of the object is proportional to its weight

22. An object is shot vertically upward. While it is rising: a. its velocity and acceleration are both upward b. its velocity is upward and its acceleration is downward c. its velocity and acceleration are both downward d. its velocity is downward and its acceleration is upward e. its velocity and acceleration are both decreasing

23. The Steamboat Geyser in Yellowstone National Park, Wyoming is capable of shooting its hot water up from the ground with a speed of 48.0 mIs. How high can this geyser shoot?

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24. A baby blue jay sits in a tall tree awaiting the arrival of its dinner. As the mother lands on the nest, she drops a worm toward the hungry chick’s mouth, but the worm misses and falls from the nest to the ground in 1.50 s. How high up is the nest?

25. At Six Flags Great Adventure Amusement Park in New Jersey, a popular ride known as “Free Fall” carries passengers up to a height of 33.5 m and drops them to the ground inside a small cage. How fast are the passengers going at the bottom of this exhilarating journey?

26. A unique type of basketball is played on the planet Zarth. During the game, a player flies above the basket and drops the ball in from a height of 10 m. If the ball takes 5.0 s to fall, find the acceleration due to gravity on Zarth.

27. Pepe, the clown, is jumping on a trampoline as Babette, the tightrope walker, above him suddenly loses her balance and falls off the tightrope straight toward Pepe. Pepe has just started upward at 15 m/s when Babette begins to fall. Pepe catches her in midair after 1.0 s. a) How far has Babette fallen when she is caught by Pepe? b) What is Babette’s velocity at the time of contact? c) What is Pepe’s velocity at the time of contact? d) How far above the trampoline was Babette before she fell?

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28. Mr. DeFronzo has just learned that he won the Presidential Award for Excellence in Science Teaching. He runs to the open window and throws his red marking pen into the air with an initial upward speed of 5.00 m/s. a) If the window is 12.0 m above the ground, what is the velocity of the pen 1.0 s after it is thrown? b) How far has the pen fallen from its starting position after 2.0 s? c) How long does it take the pen to hit the ground?