Question 1

Given the velocity-time graph for a moving box, at which point does the box change direction?

Accepted Answer

At point C, where the velocity crosses zero.

Question 2

Which section of the velocity-time graph indicates the box is speeding up in the positive direction?

Accepted Answer

Where the velocity is positive and the slope is positive.

Question 3

If the velocity-time graph has a constant positive slope, what can be said about the box's acceleration?

Accepted Answer

The acceleration is constant and positive: $$a = \frac{dv}{dt} \u003e 0$$

Question 4

At which point on the graph is the box at rest?

Accepted Answer

At the point where $$v = 0$$

Question 5

If the velocity-time graph is a straight horizontal line above the time axis, what does this indicate about the box's motion?

Accepted Answer

The box is moving at constant positive velocity.

Question 6

How do you determine the displacement of the box from a velocity-time graph between two times $$t_1$$ and $$t_2$$?

Accepted Answer

By calculating the area under the curve between $$t_1$$ and $$t_2$$: $$\Delta x = \int_{t_1$}^{t_2$} v(t) \, dt$$

Question 7

If the velocity-time graph shows a negative slope while velocity is positive, what is happening to the box?

Accepted Answer

The box is slowing down in the positive direction.

Question 8

Which feature of the velocity-time graph indicates the box is accelerating the fastest?

Accepted Answer

Where the slope of the graph is steepest.

Question 9

If the velocity-time graph is below the time axis and has a negative slope, what does this indicate?

Accepted Answer

The box is speeding up in the negative direction.

Question 10

A box moves such that its velocity-time graph is a straight line passing through the origin with positive slope. What is the box's acceleration?

Accepted Answer

The acceleration is constant and positive.

Question 11

If the velocity-time graph is a curve that is concave up, what does this say about the box's acceleration?

Accepted Answer

The acceleration is increasing.

Question 12

At which point on the velocity-time graph is the box's acceleration zero?

Accepted Answer

Where the graph is flat (horizontal line).

Question 13

If the velocity-time graph is a straight line with negative slope, what is the sign of the acceleration?

Accepted Answer

Negative: $$a = \frac{dv}{dt} \u003c 0$$

Question 14

A box starts at rest and its velocity-time graph shows a straight line with positive slope. What is the box's displacement after time $$t$$?

Accepted Answer

Displacement: $$x = \frac{1}{2} a t^2$

Question 15

If the velocity-time graph is a horizontal line below the time axis, what does this indicate about the box's motion?

Accepted Answer

The box is moving at constant negative velocity.

Question 16

How can you tell from a velocity-time graph that the box is turning around?

Accepted Answer

Where the velocity crosses zero.

Question 17

If the velocity-time graph is a curve and the slope is increasing, what does this indicate about the box's acceleration?

Accepted Answer

The acceleration is increasing.

Question 18

A box's velocity-time graph shows a section where the velocity is negative and the slope is positive. What is happening to the box?

Accepted Answer

The box is slowing down in the negative direction.

Question 19

If the velocity-time graph is a straight line with zero slope, what is the box's acceleration?

Accepted Answer

Zero: $$a = 0$$

Question 20

Which of the following best describes the relationship between the slope of a velocity-time graph and acceleration?

Accepted Answer

Acceleration is the slope of the velocity-time graph: $$a = \frac{dv}{dt}$$

Interpreting Velocity-Time Graphs: Position, Velocity, and Acceleration

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