Question 1

Which of the following best describes the instantaneous velocity at a point on a position vs. time graph?

Accepted Answer

It is the slope of the tangent line to the curve at that point.

Question 2

Given the position function $$x(t) = 4t^2$ + 2t$$, what is the instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = 4t + 2$$; at $$t=3$$, $$v = 14 m/s$$

Question 3

If the velocity vs. time graph of an object is a straight horizontal line above the time axis, what can you conclude about the object's motion?

Accepted Answer

The object is moving with constant velocity.

Question 4

An object moves such that its position vs. time graph is a straight line with a negative slope. Which statement is true?

Accepted Answer

The object is moving in the negative x-direction with constant velocity.

Question 5

For the position vs. time graph shown as a parabola opening downward (like a projectile), what is true about the velocity at the peak of the curve?

Accepted Answer

The velocity is zero.

Question 6

If the area under a velocity vs. time graph between $$t_1$$ and $$t_2 is $$negative, what does this indicate about the object's displacement?

Accepted Answer

The object moved in the negative x-direction.

Question 7

A car travels such that its position vs. time graph is a curve with increasing positive slope. What does this indicate about the car's motion?

Accepted Answer

The car is accelerating in the positive x-direction.

Question 8

Which of the following is the correct formula for average velocity over a time interval $$\Delta t$$?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 9

An object’s position vs. time graph is flat (horizontal) between $$t = 2 s $$and $$t = 5 s. $$What is true about the object during this interval?

Accepted Answer

The object is at rest.

Question 10

A runner’s velocity vs. time graph shows a straight line sloping downward, crossing the time axis from positive to negative velocity. What does this indicate?

Accepted Answer

The runner is slowing down, stops, and then reverses direction.

Question 11

If an object’s velocity is zero at a certain instant, what can you conclude about its position at that instant?

Accepted Answer

The object is at a maximum or minimum of its position vs. time graph.

Question 12

A cyclist’s position vs. time graph is a straight line with a slope of $$5 m/s. $$What is the cyclist’s velocity?

Accepted Answer

$$5 m/s$$

Question 13

Which of the following statements about the relationship between position, velocity, and time is correct?

Accepted Answer

The displacement over a time interval is the net area under the velocity vs. time graph.

Question 14

A car’s position vs. time graph is a curve that becomes less steep as time increases. What does this indicate about the car’s motion?

Accepted Answer

The car is slowing down.

Question 15

If the velocity vs. time graph is below the time axis, what does this indicate about the direction of motion?

Accepted Answer

The object is moving in the negative x-direction.

Question 16

A ball is thrown straight up. Its position vs. time graph is a parabola opening downward. At the top of its path, what is true about its velocity?

Accepted Answer

The velocity is zero.

Question 17

Which of the following best describes the meaning of the slope of a position vs. time graph?

Accepted Answer

It represents the object's velocity.

Question 18

If an object’s position vs. time graph is a straight line parallel to the time axis, what is true about the object?

Accepted Answer

The object is at rest.

Question 19

A car moves such that its velocity vs. time graph is a straight line with a positive slope. What does this indicate about the car’s motion?

Accepted Answer

The car is accelerating in the positive x-direction.

Graphing Position and Velocity: The Velocity-Position Relationship

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