CHAPTER 3 Accelerated Motion - Mr. Nguyen's Website

1 CHAPTER . 3 Accelerated Motion Practice Problems 3. Refer to the v-t graph of the toy train in Figure 3-6 to answer the following Acceleration questions. pages 57 64 page 61 Velocity (m/s). 1. A dog runs into a room and sees a cat at the other end of the room. The dog instantly stops running but slides along the wood floor until he stops, by slowing down with a constant acceleration. Sketch a Motion dia- gram for this situation, and use the velocity vectors to find the acceleration vector. Time (s). Figure 3-6. 1 2 3. Time a. When is the train's speed constant? interval v1 v2 v3. Velocity to s Position Start Stop b. During which time interval is the train's v2 acceleration positive? !v1 to s a c. When is the train's acceleration most negative? 2. Figure 3-5 is a v-t graph for Steven as he to s walks along the midway at the state fair.

2 Sketch the corresponding Motion diagram, 4. Refer to Figure 3-6 to find the average Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. complete with velocity vectors. acceleration of the train during the follow- ing time intervals. a. s to s Velocity (m/s). 2 1 v "v a! ! ! t "t 2 1. m/s " m/s ! !!! s " s ! m/s2. 0 1 2 3 4 5 6 7 8 9 10. Time (s). b. s to s 2 1 v "v Figure 3-5 a! ! ! t "t 2 1. m/s " m/s Time (s) 0 1 2 3 4 56 8 9 10 ! !!! s " s 7. ! " m/s2. c. s to s 2 1 v "v a! ! ! t "t 2 1. Physics: Principles and Problems Solutions Manual 29. CHAPTER 3 continued m/s " m/s a. What is the average acceleration of the ! !!! s " s bus while braking? ! m/s2 "v a! ! !! "t 5. Plot a v-t graph representing the following m/s " 25 m/s ! !!! ! " m/s2. Motion . An elevator starts at rest from the s ground floor of a three-story shopping b.

3 If the bus took twice as long to stop, mall. It accelerates upward for s at a how would the acceleration compare rate of m/s2, continues up at a con- with what you found in part a? stant velocity of m/s for s, and half as great (" m/s2). then experiences a constant downward acceleration of m/s2 for s as it 10. Rohith has been jogging to the bus stop for reaches the third floor. min at m/s when he looks at his watch and sees that he has plenty of time before the bus arrives. Over the next s, Velocity (m/s). he slows his pace to a leisurely m/s. What was his average acceleration during this s? "v a! ! !! "t m/s " m/s ! !!! Time (s) s ! " m/s2. page 64 11. If the rate of continental drift were to 6. A race car's velocity increases from m/s abruptly slow from cm/yr to cm/yr to 36 m/s over a time interval. What is over the time interval of a year, what would its average acceleration?

4 Be the average acceleration? Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. "v 36 m/s " m/s "v cm/yr " cm/yr a! ! !! ! !!! ! m/s2 a! ! !! ! !!! "t s "t yr 7. The race car in the previous problem slows ! " cm/yr2. from 36 m/s to 15 m/s over s. What is its average acceleration? "v 15 m/s " 36 m/s Section Review a! ! !! ! !! ! " m/s2. "t s Acceleration pages 57 64. 8. A car is coasting backwards downhill at a page 64. speed of m/s when the driver gets the 12. Velocity-Time graph What information engine started. After s, the car is moving can you obtain from a velocity-time graph ? uphill at m/s. If uphill is chosen as the positive direction, what is the car's average The velocity at any time, the time at acceleration? which the object had a particular velocity, the sign of the velocity, and the "v m/s " (" m/s).

5 A! ! !! ! !!! ! m/s2 displacement. "t s 13. Position-Time and Velocity-Time Graphs 9. A bus is moving at 25 m/s when the driver Two joggers run at a constant velocity of steps on the brakes and brings the bus to a m/s toward the east. At time t " 0, one stop in s. 30 Solutions Manual Physics: Principles and Problems CHAPTER 3 continued is 15 m east of the origin and the other is 16. Average Velocity and Average Acceleration 15 m west. A canoeist paddles upstream at 2 m/s and a. What would be the difference(s) in the then turns around and floats downstream at position-time graphs of their Motion ? 4 m/s. The turnaround time is 8 s. Both lines would have the same a. What is the average velocity of the canoe? slope, but they would rise from the Choose a coordinate system with d-axis at different points, #15 m, the positive direction upstream.

6 And "15 m. v #v i f v! ! ! b. What would be the difference(s) in their 2. velocity-time graphs? 2 m/s # ("4 m/s). ! !!! Their velocity-time graphs would be 2. identical. ! "1 m/s b. What is the average acceleration of the 14. Velocity Explain how you would use a canoe? velocity-time graph to find the time at "v which an object had a specified velocity. a! ! !! "t Draw or imagine a horizontal line at the f v "v specified velocity. Find the point where !! !i "t the graph intersects this line. Drop a ("4 m/s) " (2 m/s). line straight down to the t-axis. This ! !!! 8s would be the required time. ! m/s2. 15. Velocity-Time graph Sketch a velocity-time graph for a car that goes east at 25 m/s for 17. Critical Thinking A police officer clocked 100 s, then west at 25 m/s for another 100 s. a driver going 32 km/h over the speed limit just as the driver passed a slower car.

7 Both 25 drivers were issued speeding tickets. The judge agreed with the officer that both were Velocity (m/s). Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. guilty. The judgement was issued based on Time (s) the assumption that the cars must have 100 200 been going the same speed because they were observed next to each other. Are the "25 judge and the police officer correct? Explain with a sketch, a Motion diagram, and a position-time graph . No, they had the same position, not velocity. To have the same velocity, they would have had to have the same rela- tive position for a length of time. Physics: Principles and Problems Solutions Manual 31. CHAPTER 3 continued Sketch Position-Time graph Motion diagram Passing 4 position t0 t1 t2 t3 t4. Position 3 Faster car 2. 1. Slower car t0 t1 t2 t3 t4.

8 0. t1 t2 t3 t4. Time Practice Problems Motion with Constant Acceleration pages 65 71. page 65. 18. A golf ball rolls up a hill toward a miniature-golf hole. Assume that the direction toward the hole is positive. a. If the golf ball starts with a speed of m/s and slows at a constant rate of m/s2, what is its velocity after s? vf ! vi # at ! m/s # (" m/s2)( s). ! m/s b. What is the golf ball's velocity if the constant acceleration continues for s? Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. vf ! vi # at ! m/s # (" m/s2)( s). ! " m/s c. Describe the Motion of the golf ball in words and with a Motion diagram. The ball's velocity simply decreased in the first case. In the second case, the ball slowed to a stop and then began rolling back down the hill. Time interval 1 2 3 4.

9 Velocity #d Position Velocity Time interval 6 5. 19. A bus that is traveling at km/h speeds up at a constant rate of m/s2. What velocity does it reach s later? vf ! vi # at ! km/h # ( m/s2)( s)!!!"!!!". 1 km 3600 s 1000 m 1h ! 120 km/h 32 Solutions Manual Physics: Principles and Problems CHAPTER 3 continued 20. If a car accelerates from rest at a constant b. s m/s2, how long will it take for the car to At s, v ! 78 m/s reach a velocity of 28 m/s? c. s vf ! vi # at At s, v ! 80 m/s vf " vi so t ! ! ! a 23. Use dimensional analysis to convert an 28 m/s " m/s airplane's speed of 75 m/s to km/h. ! !!! 2 m/s (75 m/s)!!!"!!!" ! $102 km/h 3600 s 1 km ! s 1h 1000 m 21. A car slows from 22 m/s to m/s at a 24. A position-time graph for a pony running constant rate of m/s2. How many in a field is shown in Figure 3-12.

10 Draw seconds are required before the car is the corresponding velocity-time graph using traveling at m/s? the same time scale. vf ! vi # at #y Displacement (m). f v "v so t ! ! !i a m/s " 22 m/s ! !!! 2 " m/s Time (s) #x ! s Figure 3-12. page 67 #y Position-time graph 22. Use Figure 3-11 to determine the velocity Displacement (m). of an airplane that is speeding up at each of Velocity (m/s). Speeds the following times. up 82. Time (s). Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 80 #x Stops and Velocity (m/s). 78 Speeds Slows turns around up down 76. 74. 25. A car is driven at a constant velocity of 72 25 m/s for min. The car runs out of gas 70 and the driver walks in the same direction at m/s for min to the nearest gas Time (s) station. The driver takes min to fill a Figure 3-11 gasoline can, then walks back to the car at graph B represents constant speed.