Question 1

Given a position-time graph, what does the slope of the graph at any point represent?

Accepted Answer

The object's velocity at that point

Question 2

On a position-time graph, if the curve is concave down (curving downward), what can you say about the acceleration?

Accepted Answer

The acceleration is negative

Question 3

At which point on a position-time graph does the object change direction?

Accepted Answer

Where the slope of the graph is zero

Question 4

If an object’s position-time graph is a straight line with a positive slope, what does this indicate about the object’s motion?

Accepted Answer

The object is moving with constant positive velocity

Question 5

Suppose a car’s position-time graph is a parabola opening upwards. What can you conclude about the car’s acceleration?

Accepted Answer

The acceleration is positive

Question 6

At a certain point on a position-time graph, the slope is negative and the curvature is positive. What does this mean for the object’s velocity and acceleration?

Accepted Answer

Velocity is negative, acceleration is positive

Question 7

A runner’s position-time graph shows a segment where the curve is flat (horizontal). What does this indicate about the runner’s motion during that segment?

Accepted Answer

The runner is at rest

Question 8

If two objects have position-time graphs that intersect at $$t = 2\ \mathrm{s}$$, what does this mean?

Accepted Answer

The objects have the same position at $$t = 2\ \mathrm{s}$$

Question 9

A cyclist’s position-time graph is steeper at $$t = 4\ \mathrm{s}$$ than at $$t = 2\ \mathrm{s}. $$What does this indicate?

Accepted Answer

The cyclist’s velocity is greater at $$t = 4\ \mathrm{s}$$

Question 10

At point P on a position-time graph, the slope is zero and the curvature is negative. What is true about the object’s motion at point P?

Accepted Answer

The object is at rest and has negative acceleration

Question 11

A ball is thrown straight up and its position-time graph is a parabola opening downward. At the peak of its flight, what is true about its velocity and acceleration?

Accepted Answer

Velocity is zero, acceleration is negative

Question 12

If the position-time graph of a car is a straight line with a negative slope, what does this tell you about the car’s motion?

Accepted Answer

The car is moving with constant negative velocity

Question 13

On a position-time graph, which feature indicates the object is speeding up?

Accepted Answer

The slope is increasing in magnitude

Question 14

A position-time graph for a car shows a segment where the curve changes from concave up to concave down. What does this indicate?

Accepted Answer

The car’s acceleration changes sign

Question 15

If a position-time graph is a straight horizontal line, what is the object’s velocity and acceleration?

Accepted Answer

Velocity is zero, acceleration is zero

Question 16

A car’s position-time graph is a curve with a negative slope that becomes less steep over time. What does this indicate about the car’s motion?

Accepted Answer

The car is moving backward and slowing down

Question 17

At which point on a position-time graph is the object’s speed the greatest?

Accepted Answer

Where the slope is steepest (regardless of sign)

Question 18

If two objects have the same slope on their position-time graphs at a given time, what does this mean?

Accepted Answer

They have the same velocity

Question 19

A position-time graph for a train shows a segment where the curve is getting steeper and curving upward. What does this indicate about the train’s motion?

Accepted Answer

The train is speeding up with positive acceleration

Question 20

A position-time graph for a car shows a segment where the curve is getting less steep and curving downward. What does this indicate about the car’s motion?

Accepted Answer

The car is slowing down with negative acceleration

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

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