kinematics 1 - displacement & average ... 1 kinematics 1 - displacement & average velocity 1. after
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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 g