Deck 2: Motion Along a Straight Line

Question 1

The average speed is computed by

A) multiplying the acceleration by the distance traveled.
B) dividing the distance traveled by the acceleration.
C) dividing the distance traveled by the time interval.
D) multiplying the time interval by the distance traveled.

Answer 1

dividing the distance traveled by the time interval.

Question 2

A car travels 80 km in one hour. The average speed of the car is

A) 80 m/s.
B) 48 m/s.
C) 58 m/s.
D) 22 m/s.

Answer 2

22 m/s.

Question 3

A car is traveling with an average speed of 30 m/s. If the driver drives for eight hours, the distance she will cover is

A) 860 km.
B) 920 km.
C) 300 km.
D) 540 km.

Answer 3

860 km.

Question 4

A car traveling at an average speed of 25 m/s covers a distance of 900 km. The time required to travel this distance was

A) 8 hours.
B) 7 hours.
C) 9 hours.
D) 10 hours.

Question 5

A car is traveling in a straight line along the $x$ axis. At time $t = 2.1 \mathrm {~s}$ , the position is $x = 3.9 \mathrm {~m}$ ; and at time $t = 5.6 \mathrm {~s}$ , the position is $x = 52.8 \mathrm {~m}$ . The average velocity of the car is

A) 11 m/s.
B) 14 m/s.
C) 18 m/s.
D) 22 m/s.

Question 6

A runner, running in a straight line, travels 1.4 km in three minutes. The runner then turns around and runs back to her original position in four minutes. The average speed of the runner is

A) 6.7 m/s.
B) 9.9 m/s.
C) 8.5 m/s.
D) 0 m/s.

Question 7

A runner, running in a straight line, travels 1.4 km in three minutes. The runner then turns around and runs back to her original position in four minutes. The average velocity of the runner is

A) 6.7 m/s.
B) 9.9 m/s.
C) 8.5 m/s.
D) 0 m/s.

Question 8

A car is traveling at an initial velocity of 15 m/s along a straight road; it begins to accelerate at a constant rate. Forty seconds later the velocity of the car is 28 m/s (in the same direction). The average velocity of the car during the 40-second interval is

A) 15 m/s.
B) 28 m/s.
C) 22 m/s.
D) 0 m/s.

Question 9

A truck is traveling at 23 m/s. The velocity of the truck in km/h is

A) 55 km/h.
B) 83 km/h.
C) 64 km/h.
D) 23 km/h.

Question 10

The position of a particle along the x axis is given by $x ( t ) = 5 t + 3 t ^ { 2 }$ , where t is in seconds and x(t) is in meters. The velocity of the particle at time t = 5 seconds is

A) 55 m/s.
B) 48 m/s.
C) 62 m/s.
D) 35 m/s.

Question 11

The position of a particle along the $x$ axis is given by $x ( t ) = 16 t - 2 t ^ { 2 }$ , where $t$ is in seconds and $x ( t )$ is in meters. The velocity of the particle at time $t = 4$ seconds is

A) 0 m/s.
B) 16 m/s.
C) 4 m/s.
D) 8 m/s.

Question 12

A vehicle travels for four hours at a speed of 54 m/s. The vehicle then travels for two hours at a speed of 47 m/s. The average speed of the vehicle during the entire six hours is

A) 51 m/s.
B) 47 m/s.
C) 48 m/s.
D) 52 m/s.

Question 13

A vehicle travels for four kilometers at a speed of 54 m/s. The vehicle then travels for two kilometers at a speed of 47 m/s. The average speed of the vehicle during the entire six-kilometer distance is

A) 51 m/s.
B) 47 m/s.
C) 48 m/s.
D) 52 m/s.

Question 14

Two people, 100 m apart, begin walking toward each other. One person walks at 3 m/s and the other person walks at 2.3 m/s. The time (seconds) at which they will meet is

A) 16 seconds.
B) 19 seconds.
C) 21 seconds.
D) 20 seconds.

Question 15

Two people, 100 m apart, begin walking toward each other. One person walks at 3 m/s and the other person walks at 2.3 m/s. When they meet, the distance covered by the faster walker is

A) 45 m.
B) 55 m.
C) 57 m.
D) 61 m.

Question 16

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). The quickest (shortest) time at which the woman can catch the bus is

A) 3 seconds.
B) 4 seconds.
C) 7 seconds.
D) 8 seconds.

Question 17

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). The latest (longest) time at which the woman can catch the bus is

A) 3 seconds.
B) 4 seconds.
C) 7 seconds.
D) 8 seconds.

Question 18

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). When the woman first catches the bus, the velocity of the bus is

A) 2 m/s.
B) 5 m/s.
C) 3 m/s.
D) 4 m/s.

Question 19

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). When the woman and the bus meet at the second instance (second location), the velocity of the bus is

A) 5 m/s.
B) 4 m/s.
C) 6 m/s.
D) 7 m/s.

Question 20

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). When the woman first catches the bus, how far away is she (or the bus) from the bus stop?

A) 16 m
B) 11 m
C) 7.8 m
D) 4.8 m

Question 21

A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). When the woman and the bus meet at the second instance (second location), how far away is she (or the bus) from the bus stop?

A) 36 m
B) 31 m
C) 25 m
D) 28 m

Question 22

The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The initial ( $t = 0$ E) position of the particle

A) is 0 m.
B) is 2.3 m.
C) is 23 m.
D) cannot be determined.

Question 23

The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The initial ( $t = 0$ ) velocity of the particle

A) is 0 m/s.
B) is 2.3 m/s.
C) is 23 m/s.
D) cannot be determined.

Question 24

The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The initial ( $t = 0$ ) acceleration of the particle

A) is 0 m/s².
B) is 2.3 m/s².
C) is 23 m/s².
D) cannot be determined.

Question 25

The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The times ( $t \geq 0$ ) where the particle is located at the origin are

A) 0 seconds, 1.2 seconds.
B) 1.2 seconds, 23 seconds.
C) 0 seconds, 4.4 seconds.
D) 4.4 seconds, 23 seconds.

Question 26

The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The (positive) time when the particle has zero velocity is

A) 1.2 seconds.
B) 2.5 seconds.
C) 2.3 seconds.
D) 23 seconds.

Question 27

All of the following quantities include the concept of the passage of time except

A) motion.
B) position.
C) velocity.
D) acceleration.

Question 28

We will always calculate the average speed correctly by simply taking half the sum of the initial and final speeds during the time interval for all of the following cases except

A) when the distance does not change.
B) when the velocity is constant.
C) when the acceleration is constant.
D) when the acceleration is not constant.

Question 29

The average velocity of a body over some time interval is equal to the instantaneous velocity of the body whenever the acceleration of the body during that time interval is

A) constant.
B) zero.
C) positive.
D) negative.

Question 30

The mathematical relationship between the acceleration and the speed of a body is precisely the same as the mathematical relationship between

A) the speed and the distance.
B) the distance and the speed.
C) the speed and the time.
D) the distance and the time.

Question 31

The slope of a graph plotting the velocity of a body versus its time of travel is equal to

A) the distance covered by the body in the time allotted.
B) the acceleration of the body at the time specified.
C) the instantaneous velocity of the body.
D) none of the above.

Question 32

If a body is falling at its terminal speed, in the next instant

A) impact must occur.
B) its acceleration must decrease.
C) its speed must remain constant.
D) none of the above.

Question 33

All of the following are valid (though perhaps unusual) units for speed except

A) meters/second.
B) miles/minute.
C) inches/year.
D) light-years.

Question 34

All of the following are valid (though perhaps unusual) units for acceleration except

A) yards/second/second.
B) miles/minute/hour.
C) centimeters/second.
D) light-years/day/day.

Question 35

All of the following are approximately correct (that is, are exact within 10%) for a body falling freely (from rest) near the surface of the Earth except

A) during each time interval of one second, its speed changes by 30 feet per second.
B) after three seconds, its speed is 100 feet per second.
C) after one second, the body has fallen 32 feet.
D) after two seconds, the body has fallen 64 feet.

Question 36

Dimensionally, correct relations among time [t], distance [x], velocity [v], and acceleration [a] include all of the following except

A) [a] = [v] $\times$ [x].
B) [v] = [a] $\times$ [t].
C) [x] = [a] $\times$ [t²].
D) [v²] = [a] $\times$ [x].

Question 37

A tourist starts along a path of total length L. He finds that in half the time allotted he has covered a distance of only L/3. This gives him an average speed of V₁. To complete the tour on schedule, his average speed for the remainder of the tour must be

A) < 2 V₁.
B) = 2 V_1.
C) > 2 V_1.
D) We have insufficient information to determine the answer unambiguously.

Question 38

A tourist starts along a path of total length L at an average speed of V₁. At the halfway point (in distance), he finds that he has used two-thirds of the time allotted for the tour. To complete the tour on schedule, his average speed for the remainder of the tour must be

A) < 2 V₁.
B) = 2 V₁.
C) > 2 V₁.
D) We have insufficient information to determine the answer unambiguously.

Question 39

For a falling body near the surface of the Earth (neglecting air drag), all of the following change with time except

A) the acceleration of the body.
B) the velocity of the body.
C) the position of the body.
D) Hold it! There are no exceptions.

Question 40

For a falling body near the surface of the Earth (explicitly including air drag), all of the following change with time except

A) the acceleration of the body.
B) the velocity of the body.
C) the position of the body.
D) the terminal speed of the body.

Question 41

A stone is thrown vertically upward. At the very top of its path, all of the following are zero except

A) its velocity.
B) its acceleration.
C) the frictional drag.
D) Hold it! There are no exceptions.

Question 42

For a body undergoing constant acceleration, all of the following change with time except

A) the slope of a graph of velocity versus time.
B) the position of the body.
C) the average velocity of the body.
D) the instantaneous velocity of the body.

Question 43

For a body that falls freely from rest, all of the following statements are true except

A) the instantaneous velocity increases in direct proportion to the falling time.
B) the distances covered in successive (equal) time intervals are proportional to the odd integers.
C) the total distance covered increases in direct proportion to the instantaneous velocity.
D) Hold it! There are no exceptions.

Question 44

For a body undergoing constant eastward acceleration along a horizontal line, any of the following are possible except

A) a westward velocity at an instant.
B) a westward velocity for an unlimited time.
C) zero net distance from a starting point at a time after motion has begun.
D) zero velocity for an instant.

Question 45

A body has a constant acceleration of 10 ft/s², an initial speed of 10 ft/s, and a final speed of 30 ft/s. Its speed is never zero. Its time of travel is

A) 1 s.
B) 2 s.
C) 3 s.
D) 4 s.

Question 46

A body has a constant acceleration of 10 ft/s², an initial speed of 10 ft/s, and a final speed of 30 ft/s. Its speed is never zero. Its average speed is

A) 10 ft/s.
B) 20 ft/s.
C) 30 ft/s.
D) 40 ft/s.

Question 47

A body has a constant acceleration of 10 ft/s², an initial speed of 10 ft/s, and a final speed of 30 ft/s. Its speed is never zero. The distance covered is

A) 10 ft.
B) 20 ft.
C) 30 ft.
D) 40 ft.

Question 48

A body has a constant acceleration of +5 ft/s², an initial speed of -10 ft/s, and a time of travel of 4 seconds. The average velocity has a magnitude of

A) +10 ft/s.
B) +20 ft/s.
C) -10 ft/s.
D) zero.

Question 49

A body has a constant acceleration of +5 ft/s², an initial speed of -10 ft/s, and a time of travel of 4 seconds. The net displacement is

A) +40 ft.
B) +80 ft.
C) -40 ft.
D) zero.

Question 50

A body has a constant acceleration of +5 ft/s², an initial speed of -10 ft/s, and a time of travel of 4 seconds. The time at which the body has an instantaneous speed of zero is

A) 1 s.
B) 2 s.
C) 3 s.
D) 4 s.

Question 51

A body has a constant acceleration of +5 ft/sec², an initial speed of -10 ft/s, and a time of travel of 4 seconds. The total distance covered is

A) 10 ft.
B) 20 ft.
C) 30 ft.
D) 40 ft.