Question 1

A car's position as a function of time is given by $$s(t). If $$the position graph is increasing, what does this indicate about the car's movement?

Accepted Answer

The car is moving away from the starting point.

Question 2

If the velocity of an object is constant, what can be said about its acceleration?

Accepted Answer

Acceleration is zero.

Question 3

Given a position-time graph $$s(t)$$, how can you determine if the object is stationary at a certain time?

Accepted Answer

The graph has a horizontal tangent at that time.

Question 4

If the velocity graph $$v(t) is $$increasing, what does this indicate about the object's acceleration?

Accepted Answer

Acceleration is positive.

Question 5

A runner starts at rest and accelerates. Which of the following best describes the shape of the position-time graph?

Accepted Answer

The graph becomes steeper as time increases.

Question 6

If an object's velocity is decreasing but still positive, what can be said about its acceleration?

Accepted Answer

Acceleration is negative.

Question 7

A cyclist moves towards the starting point. Which of the following describes the position graph?

Accepted Answer

The graph is decreasing.

Question 8

If the slope of the velocity graph $$v(t) is $$zero, what does this indicate about the object's motion?

Accepted Answer

The object is moving at constant velocity.

Question 9

A ball is thrown upward and its velocity decreases as it rises. What is the sign of its acceleration?

Accepted Answer

Negative

Question 10

Which of the following best describes the relationship between position, velocity, and acceleration?

Accepted Answer

Velocity is the derivative of position; acceleration is the derivative of velocity.

Question 11

A car moves at a constant speed. What is the shape of its position-time graph?

Accepted Answer

A straight line with constant slope.

Question 12

If the velocity graph $$v(t) is $$decreasing, what does this indicate about the object's acceleration?

Accepted Answer

Acceleration is negative.

Question 13

A train slows down as it approaches a station. Which of the following best describes its velocity and acceleration?

Accepted Answer

Velocity is decreasing; acceleration is negative.

Question 14

If an object's position graph $$s(t) is $$constant, what can be said about its velocity?

Accepted Answer

Velocity is zero.

Question 15

A rocket's velocity increases rapidly after launch. What can be said about its acceleration?

Accepted Answer

Acceleration is positive.

Question 16

If the slope of the position graph $$s(t) is $$steep and increasing, what does this indicate about the object's velocity?

Accepted Answer

Velocity is increasing.

Question 17

A car moves away from the starting point, slows down, and then stops. Which of the following best describes the position graph?

Accepted Answer

The graph increases, becomes less steep, and then levels off.

Question 18

If an object's velocity is negative and its acceleration is positive, what is happening to its speed?

Accepted Answer

The object is slowing down.

Question 19

A runner moves towards the finish line, and her velocity increases. What is the sign of her acceleration?

Accepted Answer

Positive

Question 20

If the velocity graph $$v(t) is $$constant and positive, what does this indicate about the position graph $$s(t)$$?

Accepted Answer

The position graph is a straight line with positive slope.

Position, Velocity, and Acceleration: Precalculus Study Notes

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