Unit 2 Test

Question 1

The position of an object along the x-axis is described by the formula x = 2t^ 3 − 4t. Which of the following are the correct formulas for the velocity and acceleration of the object?

Answer 1

v = 6t^ 2 − 4, a = 12t

Question 2

A woman drives 2 blocks north, stops, continues on for another 4.5 blocks, and then makes a U-turn and drives south 3.25 blocks. After stopping momentarily she drives 5.75 blocks north. Which of the following is the magnitude of the woman’s displacement and distance traveled?

Answer 2

Displacement: 9 blocks
Distance: 15.5 blocks

Question 3

Which graph best illustrates the following description of motion?
A car starts at rest, accelerates at a constant rate until it cruises at a constant speed, and then brakes at a constant rate until it is moving at a constant, very slow speed.

Answer 3

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Question 4

For the given velocity-time graph, select the corresponding position-time graph.

Answer 4

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Question 5

A track athlete runs in a 400 m race, which is once around a track. If the runner ends the race with a time of 52.5 s, which of the following is the average velocity and the average speed of the athlete?

Answer 5

average velocity: 0

average speed: 7.6 m / s

Question 6

A car travels with a speed of 3.5 m / s, and then accelerates to 5.5 m / s in 4 s. Which of the following is the average acceleration of the car?

Answer 6

0.5 m / s2

Question 7

The position of an object along the x-axis is described by the formula x = 3t ^2 − 2t. Which of the following are the correct formulas for the velocity and acceleration of the object?

Answer 7

v = 6t − 2, a = 6

Question 8

Which graph best illustrates the following description of motion?
A car starts at rest, accelerates at a constant rate until it comes up behind a motorcycle that is moving more slowly, then slows down to follow the motorcycle, maintaining a constant distance behind it. Once the motorcycle has turned, the driver of the car accelerates to a much faster speed and then maintains that speed.

Answer 8

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Question 9

A squirrel knocks an acorn loose near the top of a tree. If an observer on the ground were sitting 4 m directly below the acorn, how much time does the observer have to move out of the way before getting hit on the head?

Answer 9

0.9 s

Question 10

King Kong is holding a woman on top of a skyscraper when she suddenly slips out of his hand. How tall is the building if Superman has a minimum time of 2.30 s to catch the woman before she hits the ground?

Answer 10

25.9 m

Question 11

How fast must a baseball move as it leaves your hand if it reaches a maximum height of 15.0 m above the point where it left your hand?

Answer 11

17.1 m / s

Question 12

One person drops a ball from rest 10 m above the ground. Simultaneously, a second person throws a ball down with an initial downward velocity of 3 m / s. If the two balls hit the ground at the same time, what total vertical distance did the second ball fall?

Answer 12

14.3 meters

Question 13

A car is moving at 20 m / s before it applies the brakes for 4 s. It slows at a constant rate to 10 m / s. Five seconds after this, the brakes are applied again and stop the car in 5 seconds. The car slows at a constant rate during this period of time as well. What is the total distance the car travels from the moment the brakes were first applied to the moment it stops?

Answer 13

135m

Question 14

Given the position vector r(t) = 4t^2i + 3tj, which of the following is the acceleration vector?

Answer 14

a(t) = 8i

Question 15

If the position vector of an object is r(t) = 4t^2i - 3j, what are the instantaneous velocity vector components at t = 1s?

Answer 15

vx  = 8 m / s,
vy  = 0 m / s

Question 16

Which of the following pairs of vectors have the same direction?

Answer 16

A = 3i + 2j
B = 6i + 4j

Question 17

What is correct magnitude of the position vector for the following description of the motion of an object?

A car moves 3 blocks west, then 2 blocks north, and then 3 blocks south before stopping briefly. It then moves 1 block east and finally 2 blocks south.

Answer 17

3.6 blocks

Question 18

An airplane has an initial velocity with respect to the ground of 200 mph in an eastward direction. A strong wind begins to blow with a velocity of 80 mph from north to south. What are the x-and y-components of the total velocity of the plane when the wind is taken into account? Let north be the positive y-direction and east be the positive x-direction.

Answer 18

vx  = +200 mph
vy  = −80 mph

Question 19

If the position vector of an object is r(t) = 2t^2i - 4tj, what are the instantaneous velocity vector components at t = 2s?

Answer 19

vx  = 8 m / s
vy  = −4 m / s

Question 20

A ball rolls with a speed of 2 m / s along a horizontal table. If the ball rolls off the table and lands on the floor 0.50 m from the edge of the table, what is the height of the table?

Answer 20

0.3 m

Question 21

A soccer player kicks a ball off the ground at an angle of 30° with a total speed of 10 m / s. How far away would a teammate have to be to receive the ball when it first lands on the ground?

Answer 21

8.8 m

Question 22

At which of the following speeds would you have to throw a ball if you wanted it to reach a maximum height of 10 m above the point you released the ball? Assume you throw it at a 70° angle with respect to the horizontal.

Answer 22

14.8 m / s

Question 23

A child is guiding a toy airplane attached to a guide wire around in a circle. The plane circles with a period T. If the child pulls in the guide wire to half the original radius, while simultaneously adjusting the speed so that the period T remains constant, how has the centripetal acceleration changed?

Answer 23

The acceleration decreases by 2

Question 24

Two children are playing catch in a passenger train. An observer on the ground measures that the train is traveling at 70 mph. As the train passes the observer, he measures that the ball is thrown with half of the speed as the passenger train. What velocity do the children measure for the ball? (Assume the positive direction is the direction in which the train is moving.)

Answer 24

−35 mph

Question 25

The pilot of an airplane wishes to fly due north, but a strong wind is blowing toward the east. Which direction must the plane head in order to fly due north?

Answer 25

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