Q: A car moves according to the position vs. time graph shown in the first image. What is the velocity of the car from $$t = 10 s to$$ $$t = 40 s$$?

$$v = \frac{-30\,\text{m} - 60\,\text{m}}{40\,\text{s} - 10\,\text{s}} = \frac{-90\,\text{m}}{30\,\text{s}} = -3\,\text{m/s}$$

Q: A velocity vs. time graph forms a triangle above the time axis from $$t = 2 s to$$ $$t = 4 s $$with a peak at $$v = 2 m/s. $$What is the displacement during this interval?

$$A = \frac{1}{2} \times 2\,\text{s} \times 2\,\text{m/s} = 2\,\text{m}$$

Q: A car starts from rest and accelerates at $$2\,\text{m/s}^2$$ for $$5$$ seconds. What is its final velocity?

$$v = 2\,\text{m/s}^2 \times 5\,\text{s} = 10\,\text{m/s}$$

Q: A runner moves with a constant velocity of $$3\,\text{m/s}$$ for $$10$$ seconds. What is the total displacement?

$$\Delta x = 3\,\text{m/s} \times 10\,\text{s} = 30\,\text{m}$$

Question 1

Given a position vs. time graph, how do you determine the velocity of an object during a specific time interval?

Accepted Answer

By calculating the slope, $$m = \frac{\Delta y}{\Delta x}$$, which is $$\frac{\Delta x}{\Delta t}.$$

Question 2

A car moves according to the position vs. time graph shown in the first image. What is the velocity of the car from $$t = 10 s to$$ $$t = 40 s$$?

Accepted Answer

$$v = \frac{-30\,	ext{m} - 60\,	ext{m}}{40\,	ext{s} - 10\,	ext{s}} = \frac{-90\,	ext{m}}{30\,	ext{s}} = -3\,	ext{m/s}$$

Question 3

Which of the following best describes the motion represented by a straight, positively sloped line on a position vs. time graph?

Accepted Answer

The object is moving at a constant positive velocity.

Question 4

If the velocity vs. time graph is a horizontal line above the time axis, what does this indicate about the object's motion?

Accepted Answer

The object is moving at a constant velocity.

Question 5

How do you calculate the displacement from a velocity vs. time graph between two times?

Accepted Answer

By finding the area under the curve between the two times.

Question 6

A velocity vs. time graph forms a triangle above the time axis from $$t = 2 s to$$ $$t = 4 s $$with a peak at $$v = 2 m/s. $$What is the displacement during this interval?

Accepted Answer

$$A = \frac{1}{2} 	imes 2\,	ext{s} 	imes 2\,	ext{m/s} = 2\,	ext{m}$$

Question 7

Which of the following statements is true about the area under an acceleration vs. time graph?

Accepted Answer

It represents the object's change in velocity.

Question 8

A car starts from rest and accelerates at $$2\,	ext{m/s}^2$$ for $$5$$ seconds. What is its final velocity?

Accepted Answer

$$v = 2\,	ext{m/s}^2 	imes 5\,	ext{s} = 10\,	ext{m/s}$$

Question 9

If a position vs. time graph is a horizontal line, what does this indicate about the object's motion?

Accepted Answer

The object is at rest.

Question 10

A velocity vs. time graph shows a straight line with a negative slope. What does this indicate about the object's acceleration?

Accepted Answer

The object has a constant negative acceleration.

Question 11

A runner moves with a constant velocity of $$3\,	ext{m/s}$$ for $$10$$ seconds. What is the total displacement?

Accepted Answer

$$\Delta x = 3\,	ext{m/s} 	imes 10\,	ext{s} = 30\,	ext{m}$$

Question 12

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

Accepted Answer

The slope of a velocity vs. time graph gives the object's acceleration.

Question 13

A car's acceleration vs. time graph is a horizontal line at $$a = 2\,	ext{m/s}^2$$ from $$t = 0 to$$ $$t = 4 s. $$What is the change in velocity during this interval?

Accepted Answer

$$\Delta v = 2\,	ext{m/s}^2 	imes 4\,	ext{s} = 8\,	ext{m/s}$$

Question 14

Which of the following is true about the area under a velocity vs. time graph?

Accepted Answer

It represents the object's displacement.

Question 15

A position vs. time graph shows a curve that gets steeper as time increases. What does this indicate about the object's motion?

Accepted Answer

The object is accelerating.

Question 16

If the velocity vs. time graph is a straight line with a positive slope, what does this indicate about the object's acceleration?

Accepted Answer

The object has a constant positive acceleration.

Question 17

A car moves according to the position vs. time graph shown in the first image. During which time interval is the car at rest?

Accepted Answer

From $$t = 10 s to$$ $$t = 20 s$$

Representing Motion with Graphs: Slope and Area Models in Kinematics

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