Q: A car travels 6 meters in 3 seconds. What is its average velocity during this interval?

$$v = \frac{6\ \text{m}}{3\ \text{s}} = 2\ \text{m/s}$$

Q: A car moves 8 meters in 2 seconds, then remains motionless for 3 seconds, and finally moves -5 meters in 5 seconds. What is the velocity during the last 5 seconds?

$$v = \frac{-5\ \text{m}}{5\ \text{s}} = -1\ \text{m/s}$$

Q: A car travels 5 meters in 2 seconds, stays motionless for 2 seconds, then moves 5 meters in the opposite direction in 4 seconds. What is the velocity during the 4-second interval?

$$v = \frac{-5\ \text{m}}{4\ \text{s}} = -1.25\ \text{m/s}$$

Q: A car moves forward at $$3\ \text{m/s}$$ for 2 seconds. How far does it travel during this interval?

$$d = v \times t = 3\ \text{m/s} \times 2\ \text{s} = 6\ \text{m}$$

Question 1

A position-time graph shows a straight line with a positive slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving away from the origin at a constant velocity.

Question 2

If the slope of a position-time graph increases over time, what can you conclude about the object's motion?

Accepted Answer

The object is accelerating away from the origin.

Question 3

A car travels 6 meters in 3 seconds. What is its average velocity during this interval?

Accepted Answer

$$v = \frac{6\ 	ext{m}}{3\ 	ext{s}} = 2\ 	ext{m/s}$$

Question 4

On a position-time graph, what does a horizontal line represent?

Accepted Answer

The object is not moving; its position is constant.

Question 5

A car moves 8 meters in 2 seconds, then remains motionless for 3 seconds, and finally moves -5 meters in 5 seconds. What is the velocity during the last 5 seconds?

Accepted Answer

$$v = \frac{-5\ 	ext{m}}{5\ 	ext{s}} = -1\ 	ext{m/s}$$

Question 6

If a position-time graph shows a negative slope, what does this indicate about the object's motion?

Accepted Answer

The object is moving towards the origin.

Question 7

A car travels 5 meters in 2 seconds, stays motionless for 2 seconds, then moves 5 meters in the opposite direction in 4 seconds. What is the velocity during the 4-second interval?

Accepted Answer

$$v = \frac{-5\ 	ext{m}}{4\ 	ext{s}} = -1.25\ 	ext{m/s}$$

Question 8

How can you determine which segment of a position-time graph represents the fastest motion without calculating velocity?

Accepted Answer

The segment with the steepest slope represents the fastest motion.

Question 9

A car moves forward at $$3\ 	ext{m/s}$$ for 2 seconds. How far does it travel during this interval?

Accepted Answer

$$d = v 	imes t = 3\ 	ext{m/s} 	imes 2\ 	ext{s} = 6\ 	ext{m}$$

Question 10

If a position-time graph shows a flat segment followed by a negative slope, what does this indicate about the object's motion?

Accepted Answer

The object was stationary, then started moving towards the origin.

Question 11

A car travels 8 meters in 2 seconds, then remains motionless for 3 seconds. What is its velocity during the first 2 seconds?

Accepted Answer

$$v = \frac{8\ 	ext{m}}{2\ 	ext{s}} = 4\ 	ext{m/s}$$

Question 12

Which of the following best describes the motion of an object whose position-time graph has a small positive slope?

Accepted Answer

The object is moving slowly away from the origin.

Question 13

A car travels 5 meters in 2 seconds, stays motionless for 2 seconds, then moves 5 meters in the opposite direction in 4 seconds, and finally moves forward at $$3\ 	ext{m/s}$$ for 2 seconds. What is the total displacement after 10 seconds?

Accepted Answer

$$5\ 	ext{m} + (-5\ 	ext{m}) + 6\ 	ext{m} = 6\ 	ext{m}$$

Question 14

If a position-time graph shows a large positive slope, what does this indicate about the object's motion?

Accepted Answer

The object is moving quickly away from the origin.

Question 15

A car moves -5 meters in 5 seconds. What is its velocity?

Accepted Answer

$$v = \frac{-5\ 	ext{m}}{5\ 	ext{s}} = -1\ 	ext{m/s}$$

Question 16

Which of the following statements is true about the velocity of an object when its position-time graph is a straight line?

Accepted Answer

The velocity is constant.

Question 17

A car travels 2 meters in 2 seconds. What is its velocity?

Accepted Answer

$$v = \frac{2\ 	ext{m}}{2\ 	ext{s}} = 1\ 	ext{m/s}$$

Question 18

If a position-time graph shows a segment where the slope is zero, followed by a segment with a small negative slope, what does this indicate?

Accepted Answer

The object was stationary, then started moving slowly towards the origin.

Question 19

A car travels 6 meters in 3 seconds, stops for 5 seconds, then moves 2 meters in 2 seconds. What is the average velocity for the entire 10-second interval?

Accepted Answer

$$v_{avg} = \frac{6\ 	ext{m} + 2\ 	ext{m}}{10\ 	ext{s}} = \frac{8\ 	ext{m}}{10\ 	ext{s}} = 0.8\ 	ext{m/s}$$

Guided Practice: Position-Time Graphs in Physics with Calculus

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