1. Haiwa walks eastward with a speed of 0.98 m/s. If it takes him 34 min to walk to the store, how far has he walked?

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1 Practice 1A Average velocity and displacement 1. Haiwa walks eastward with a speed of 0.98 m/s. If it takes him 34 min to walk to the store, how far has he walked? v avg = 0.98 m/s east t = 34 min x =? 2. If Hooker rides south his bicycle in a straight line for 15 min with an average velocity of 12.5 km/h, what is his displacement? t = 15 min v avg = 12.5 km/h south x =? 3. It takes you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement? t = 9.5 min v avg = 1.2 m/s north x =? 0

2 4. Aram drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway? v avg = 48.0 km/h east x = 144 km east 5. Look back at item 4. How much time would Aram save by increasing his average velocity to 56.0 km/h to the east? v avg = 56.0 km/h east x = 144 km east time saved =? 6. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then, it travels 210 km south with an average velocity of 75 km/h to the south. a. How long does the total trip last? b. What is the average velocity for the total trip? x 1 = 280 km south v avg,1 = 88 km/h south t 2 = 24 min v avg,2 = 0 km/h x 3 = 210 km south v avg,3 = 75 km/h south 1

3 t tot =? v avg, tot =? Section Review What is the shortest possible time in which a bacterium could drift at a constant speed of 3.5 mm/s across a Petri dish with a diameter of 8.4 cm? v = 3.5 mm/s x = 8.4 cm 2. A child is pushing a shopping cart at a speed of 1.5 m/s. How long will it take this child to push the cart down an aisle with a length of 9.3 m? v = 1.5 m/s x = 9.3 m 3. An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 s and makes the return trip to the starting position in 22.0 s. a. What is the average velocity for the first half of the swim? b. What is the average velocity for the second half of the swim? c. What is the average velocity for the roundtrip? x 1 = 50.0 m south t 1 = 20.0 s x 2 = 50.0 m north t 2 = 22.0 s v avg,1 =? v avg,2 =? v avg =? c. 2

4 4. Two students walk in the same direction along a straight path, at 0.90 m/s and the other at 1.90 m/s. a. Assuming that they start at the same point and the same time, how much sooner does the faster student arrive at a destination 780 m away? b. How far would the students have to walk so that the faster student arrives 5.50 min before the slower student? v 1 = 0.90 m/s v 2 = 1.90 m/s x = 780 m t 1 t 2 = (5.50 min)(60 s/min) = s t 1 t 2 =? x 1 =? x 2 =? 5. Critical Thinking Does knowing the distance between two objects give you enough information to locate the objects? Explain. No, because a single distance could correspond to a variety of different positions of the objects 3

5 6. Interpreting Graphics Figure 1-8 shows position-time graphs of the straightline movement of two deer A and B in a wildlife preserve. Which deer has the greater average velocity over the entire period? Which deer has the greater velocity at t = 8.0 min? Is the velocity of deer A always positive? Is the velocity of deer B ever negative? Deer A Deer B deer B; deer A; no; no Practice 1B Average acceleration 1. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at 4.1 m/s 2 as it slows from 9.0 m/s to 0.0 m/s. What is the time needed for the bus to stop? a avg = 4.1 m/s 2 v i = 9.0 m/s v f = 0.0 m/s 4

6 2. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s 2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? a avg = 2.5 m/s 2 v i = 7.0 m/s v f = 12.0 m/s 3. A cyclist reduces his speed from 6.5 m/s to 0.0 m/s with an acceleration of 1.2 m/s 2. How long does that take? a avg = 1.2 m/s 2 v i = 6.5 m/s v f = 0.0 m/s 4. The velocity of a bicycle is changed from 1.2 m/s to 6.5 m/s during 25 min. What is its acceleration? V i = 1.2 m/s V f = 6.5 m/s t = 25 min 5. Suppose that the bicycle in item 4 has an average acceleration of m/s 2 a. How much does its speed change after 5.0 min? b. If the treadmill s initial speed is 1.7 m/s, what will its final speed be? a avg = m/s 2 t = 5.0 min v i = 1.7 m/s v =? v f =? 5

7 Practice 1C Displacement with constant uniform acceleration 1. A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. What is the distance covered by the car? v i = 0.0 m/s v f = 6.6 m/s t = 6.5 s x =? 2. When Zilan applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes in order to stop at the sign? v i = 15.0 m/s v f = 0.0 m/s t = 2.50 s x =? 3. A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to a stop in exactly 99 m? v i = 21.8 m/s x = 99 m v f = 0.0 m/s 4. A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast (in m/s) is the car moving after this time? v i = 6.4 m/s x = 3.2 km t = 3.5 min v f =? 6

8 Practice 1D Velocity and displacement with uniform acceleration 1. A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s 2 for 3.6 s. Find the final speed and the displacement of the car during this time. v i = 6.5 m/s a = 0.92 m/s 2 t = 3.6 s v f =? x =? 2. An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.00 m/s 2. Find the final speed and the displacement after 5.00 s. v i = 4.30 m/s a = 3.00 m/s 2 t = 5.00 s v f =? x =? 3. A car starts from rest and travels for 5.0 s with a constant acceleration of 1.5 m/s 2. What is the final velocity of the car? How far does the car travel in this time interval? v i = 0.0 m/s t = 5.0 s a = 1.5 m/s 2 v f =? x =? 4. A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of 2.0 m/s 2. How long does it take the car to accelerate to a 7

9 final speed of 10.0 m/s? How far has the car moved during the braking period? v i = 15.0 m/s a = 2.0 m/s 2 v f = 10.0 m/s x =? Practice 1E Find velocity after any displacement 1. Find the velocity after the stroller in Sample Problem 1E has traveled 6.32 m. a = m/s 2 x = 6.32 m v f =? 2. A car traveling initially at +7.0 m/s accelerates uniformly at the rate of m/s 2 for a distance of 245 m. a. What is its velocity at the end of the acceleration? b. What is its velocity after it accelerates for 125 m? c. What is its velocity after it accelerates for 67 m? v i =+7.0 m/s a =+0.80 m/s 2 x = 245 m v f =? x = 245 m 8

10 x = 125 m x = 76 m 3. A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s 2. a. What is the speed of the car after it has traveled 55 m? b. How long does it take the car to travel 55 m? a = 2.3 m/s 2 x = 55 m v f =? 4. A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s 2 to the east, how far did it travel during the acceleration? v i = 6.5 m/s v f = 1.5 m/s a = 2.7 m/s 2 x =? 5. An aircraft has a liftoff speed of 120 km/h. What minimum uniform acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m? 9

11 v i = 0.0 m/s v f = 120 km/h =120x(1000/60x60) = 33 m/s x = 240 m a =? 6. A certain car is capable of accelerating at a uniform rate of 0.85 m/s 2. What is the magnitude of the car s displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h? a = 0.85 m/s 2 v i = 83 km/h v f = 94 km/h x =? 10

12 Section Review A car accelerates uniformly at a rate of m/s 2. How long does it take for the car to accelerate from a speed of 88.5 km/h to a speed of 96.5 km/h? a =+2.60 m/s 2 v i = 88.5 km/h = 88.5 x (1000/3600) = 24.6 m/s v f = 96.5 km/h = 96.5 x (1000/3600) = 26.8 m/s 2. A ball with a negative initial velocity slows down as it rolls down on a straight path. Is the ball s acceleration positive or negative? Ans: positive 3. Karzan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s. a. What is Karzan s acceleration? b. What is Karzan s displacement during this time interval? c. What is Karzan s average velocity during this time interval? v f = 12.5 m/s t = 2.5 s a =? x =? V avg =? 4. Critical Thinking Two cars A and B are moving in the same direction in parallel lines along a highway. At some instant, the instantaneous velocity of car A exceeds the instantaneous velocity of car B. Does this mean that car A s acceleration is greater than car B s? Explain, and use examples. 11

Ans: No, car A s acceleration is not necessarily greater than car B s acceleration; If the two cars are moving in the positive direction, car A could be slowing down (negative acceleration) while car

13 Ans: No, car A s acceleration is not necessarily greater than car B s acceleration; If the two cars are moving in the positive direction, car A could be slowing down (negative acceleration) while car B is speeding up (positive acceleration), even though car A s velocity is greater than car B s velocity. 5. Interpreting Graphics The velocity-versus-time graph for a shuttle bus moving along a straight path is shown in Figure a. Identify the time intervals during which the velocity of the shuttle bus is constant. Ans: 0 s to 30 s; 60 s to 125 s; 210 s to 275 s b. Identify the time intervals during which the acceleration of the shuttle bus is constant. Ans: 0 s to 30 s; 30 s to 60 s; 60 s to 125 s; 125 s to 210 s; 210 s to 275 s; 275 s to 300 s; 300 s to 520 s; 520 s to 580 s c. Find the value for the average velocity of the shuttle bus during each time interval identified in b. Ans: 0 m/s; 1.5 m/s; 0 m/s; 1.5 m/s; 0 m/s; 0.75 m/s; 3.25 m/s; 4.5 m/s d. Find the acceleration of the shuttle bus during each time interval identified in b. Ans: 0 m/s 2 ; 0.1 m/s 2 ; 0 m/s 2 ; 0.04 m/s 2 ; 0 m/s 2 ; 0.06 m/s 2 ; 0.02 m/s 2 ; 0.02 m/s 2 e. Identify the times at which the velocity of the shuttle bus is zero. Ans: 0 to 30 s; 210 to 275 s f. Identify the times at which the acceleration of the shuttle bus is zero. Ans: 0 s to 30s; 60 s to 125 s; 210 s to 275 s g. Explain what the slope of the graph reveals about the acceleration in each time interval. 12

14 Ans: When the graph slopes upward, acceleration is positive. When it slopes downward, acceleration is negative. 6. Interpreting Graphics Is the shuttle bus in item 5 always moving in the same direction? Explain, and refer to the time intervals shown on the graph. Ans: No; The bus is moving in the positive direction from 30 s to 210 s (when velocity is positive) and in the negative direction from 275 s to 600 s (when velocity is negative). 13

15 Practice 1F Falling object 1. A robot probe drops a camera off the rim of a 239 m high cliff on Mars, where the free-fall acceleration is 3.7 m/s 2. a. Find the velocity with which the camera hits the ground. b. Find the time required for it to hit the ground. y = 239 m a = 3.7 m/s 2 v f =? 2. A flowerpot falls from a windowsill 25.0 m above the sidewalk. a. How fast is the flowerpot moving when it strikes the ground? b. How much time does a passerby of height 1.8 m on the sidewalk below have to move out of the way before the flowerpot hits the ground? y = 25.0 m a = 9.81 m/s 2 v f =? 3. A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. a. What will the ball s speed be when it returns to its starting point? b. How long will the ball take to reach its starting point? v i =+8.0 m/s a = 9.81 m/s 2 y = 0 m v f =? 14

16 4. Calculate the displacement of the volleyball in Sample Problem 1F when the volleyball s final velocity is 1.1 m/s upward. v i =+6.0 m/s v f =+1.1 m/s a = 9.81 m/s 2 y =? Section Review A coin is tossed vertically upward. a. What happens to its velocity while it is in the air? Ans: The coin s velocity decreases, becomes zero at its maximum height, and then increases in the negative direction until the coin hits the ground. b. Does its acceleration increase, decrease, or remain constant while it is in the air? Ans: The coin s acceleration remains constant. 2. A pebble is dropped down a well and hits the water 1.5 s later. Using the equations for motion with constant acceleration, determine the distance from the edge of the well to the water s surface. t = 1.5 s a = 9.81 m/s 2 y =? 3. A ball is thrown vertically upward. What are its velocity and acceleration when it reaches its maximum altitude? What is its acceleration just before it hits the ground? Ans: At maximum altitude, v = 0 and a = 9.81 m/s 2 ; Just before the ball hits the ground, a = 9.81 m/s 2. 15

4. Two children are bouncing small rubber balls. One child simply drops a ball. At the same time, the second child throws a ball downward so that it has an initial speed of 10 m/s.

17 4. Two children are bouncing small rubber balls. One child simply drops a ball. At the same time, the second child throws a ball downward so that it has an initial speed of 10 m/s. What is the acceleration of each ball while in motion? Ans: 9.81 m/s 2 for each ball. 5. Critical Thinking A gymnast practices two dismounts from the high bar on the uneven parallel bars. During one dismount, he swings up off the bar with an initial upward velocity of m/s. In the second, he releases from the same height but with an initial downward velocity of 3.0 m/s. Compare the final velocities of the gymnast as he reaches the ground. What is his acceleration in each case? Ans: The gymnast s acceleration ( 9.81 m/s 2 ) will be the same in each case. His final velocities will be determined by the equation v f 2 = v i 2 +2a y. Because the acceleration and displacement are the same, the final velocity is greater for the larger initial velocity, +4.0 m/s. 6. Interpreting Graphics Figure 1-17 is a position-time graph of the motion of a basketball thrown straight up. Use the graph to sketch the path of the basketball and to sketch a velocity-time graph of the basket- ball s motion. Ans: The ball goes up 0.5 m, returns to its original position, and then falls another 5.5 m. The time axis of students graphs should follow that in Figure 1-17, and the velocity coordinates should roughly correspond to x/y in Figure 17 at each point. a. Is the velocity of the basketball constant? no b. Is the acceleration of the basketball constant? yes c. What is the initial velocity of the basketball? about 3 m/s 16

18 Chapter 2 Review and Assess Velocity and Acceleration Review questions 1. What would be the acceleration of a turtle that is moving with a constant velocity of 0.25 m/s to the right? Ans: 0.00 m/s 2 2. Sketch the velocity-time graphs for the following motions. a. a city bus that is moving with a constant velocity Ans: slope is zero b. a wheelbarrow that is speeding up at a uniform rate of acceleration while moving in the positive direction Ans: slope is positive c. a tiger that is speeding up at a uniform rate of acceleration while moving in the negative direction Ans: slope is negative d. a deer that is slowing down at a uniform rate of acceleration while moving in the positive direction Ans: slope is negative e. a horse that is slowing down at a uniform rate of acceleration while moving in the negative direction Ans: slope is positive Practice problems 3. A car traveling in a straight line has a velocity of +5.0 m/s. After an acceleration of 0.75 m/s 2, the car s velocity is +8.0 m/s. In what time interval did the acceleration occur? v i =+5.0 m/s a avg =+0.75 m/s 2 v f =+8.0 m/s 17

4. The velocity-time graph for an object moving along a straight path is shown in Figure 1-22. Find the average accelerations during the time intervals: a. 0.0 s to 5.0 s. v i = 6.8 m/s v f = 6.

19 4. The velocity-time graph for an object moving along a straight path is shown in Figure Find the average accelerations during the time intervals: a. 0.0 s to 5.0 s. v i = 6.8 m/s v f = 6.8 m/s t = 5.0 s b. 5.0 s to 15.0 s. v i = 6.8 m/s v f =+6.8 m/s t = 10.0 s c. 0.0 s to 20.0 s. v i = 6.8 m/s v f =+6.8 m/s t = 20.0 s 5. A bus slows down uniformly from 75.0 km/h (21 m/s) to 0 km/h in 21 s. How far does it travel before stopping? v i = 75.0 km/h = 21.0 m/s v f = 0 km/h = 0 m/s t = 21 s 18

20 6. A car accelerates uniformly from rest to a speed of 65 km/h (18 m/s) in 12 s. Find the distance the car travels during this time. v f = 18 m/s t = 12 s 7. A car traveling at +7.0 m/s accelerates at the rate of m/s 2 for an interval of 2.0 s. Find v f. v i =+7.0 m/s a =+0.80 m/s 2 t = 2.0 s 8. A car accelerates from rest at 3.00 m/s 2. a. What is the velocity at the end of 5.0 s? b. What is the displacement after 5.0 s? a = 3.00 m/s 2 t = 5.0 s 9. A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s 2. The driver then applies the brakes, causing a uniform acceleration of 2.0 m/s 2. If the brakes are applied for 3.0 s, a. How fast is the car going at the end of the braking period? b. How far has it gone from its start? t 1 = 5.0 s a 1 =+1.5 m/s 2 t 2 = 3.0 s a 2 = 2.0 m/s 2 19

21 10. A boy sledding down a hill accelerates at 1.40 m/s 2. If he started from rest, in what distance would he reach a speed of 7.00 m/s? a = 1.40 m/s2 v f = 7.00 m/s Falling Objects Conceptual questions 11. A ball is thrown vertically upward. a. What happens to the ball s velocity while the ball is in the air? Ans: The ball s velocity decreases, becomes zero at its maximum altitude, then increases in the negative direction. b. What is its velocity when it reaches its maximum altitude? Ans: At maximum altitude, the ball s velocity is zero. c. What is its acceleration when it reaches its maximum altitude? Ans: 9.81 m/s 2 d. What is its acceleration just before it hits the ground? Ans: 9.81 m/s 2 e. Does its acceleration increase, decrease, or remain constant? Ans: The ball s acceleration remains constant. Practice problems 12. A worker drops a wrench from the top of a tower 80.0 m tall. What is the velocity when the wrench strikes the ground? y = 80.0 m a = 9.81 m/s 2 20

22 13. A peregrine falcon dives at a pigeon. The falcon starts downward from rest with free-fall acceleration. If the pigeon is 76.0 m below the initial position of the falcon, how long does the falcon take to reach the pigeon? Assume that the pigeon remains at rest. a = 9.81 m/s 2 y = 76.0 m 21

23 Chapter 1 Standardized Test Prep Multiple Choices Use the graphs below to answer questions Which graph represents an object moving with a constant positive velocity? A. I B. II C. III D. IV 2. Which graph represents an object at rest? A. I B. II C. III D. IV 3. Which graph represents an object moving with constant positive acceleration? A. I B. II C. III D. IV 4. A bus travels from El Paso, Texas, to Chihuahua, Mexico, in 5.2 h with an average velocity of 73 km/h to the south. What is the bus s displacement? A. 73 km to the south B. 370 km to the south C. 380 km to the south D. 14 km/h to the south 22

24 t = 5.2 h v avg = 73 km/h south Use the following position-time graph of a squirrel running along a clothesline to answer questions What is the squirrel s displacement at time t = 3.0 s? A. 6.0 m B. 2.0 m C m D m t = 3.0 s 6. What is the squirrel s average velocity during the time interval between 0.0 s and 3.0 s? A. 2.0 m/s B m/s C. 0.0 m/s D m/s x = 2.0 m (see 5.) t = 3.0 s 7. Which of the following statements is true of acceleration? A. Acceleration always has the same sign as displacement. B. Acceleration always has the same sign as velocity. C. The sign of acceleration depends on both the direction of motion and how the velocity is changing. D. Acceleration always has a positive sign. 23

25 8. A ball initially at rest rolls down a hill and has an acceleration of 3.3 m/s 2. If it accelerates for 7.5 s, how far will it move during this time? A. 12 m B. 93 m C. 120 m D. 190 m a = 3.3 m/s 2 t = 7.5 s 9. Which of the following statements is true for a ball thrown vertically upward? A. The ball has a negative acceleration on the way up and a positive acceleration on the way down. B. The ball has a positive acceleration on the way up and a negative acceleration on the way down. C. The ball has zero acceleration on the way up and a positive acceleration on the way down. D. The ball has a constant acceleration through-out its flight. 24

Chapter 2: Motion in One Dimension

Assumption College English Program Mr. Stephen Dobosh s EP- M 4 P h y s i c s C l a s s w o r k / H o m e w o r k P a c k e t Chapter 2: Motion in One Dimension Section 1: Displacement and Velocity Section