Chapter 3, Problem 54A

(a)

To determine

The example of an object that is slowing down but has a positive acceleration.

Explanation of Solution

Introduction:

Acceleration is the rate of change of velocity. The change in acceleration is possible if either the speed of an object changes or the direction of the moving object changes.

Consider an example of a body standing at point $P$ which moves towards left to point $Q$ and again moves in the same direction from point $Q$ with a slowdown in speed to the point $R$ .

In the above example, the change in velocity is in right direction and for this, the acceleration will be positive.

Conclusion:

Therefore, the body is slowing down but has a positive acceleration.

(b)

To determine

The example of an object that is speeding up but has a negative acceleration.

Explanation of Solution

Introduction:

Acceleration is a vector quantity. Its direction is determined by the change in velocity. If the change in velocity is towards right, it has a positive acceleration whereas if the change in velocity is towards left, it has a negative acceleration.

Consider an example, a body standing at point $P$ moves towards left at point $Q$ and again move in the same direction from point $Q$ with a speed up to the point $R$ .

In the above example, the change in velocity is in left direction and for this the acceleration will be negative.

Conclusion:

Therefore, the body is speeding up but has a negative acceleration.

(c)

To determine

The example of an object that is moving at a constant speed but has a negative acceleration.

Explanation of Solution

Introduction:

Acceleration is a vector quantity. It depends on velocity not speed.

A body having a constant speed can have a variable velocity and thus can also have an acceleration.

Consider an example of a car starts moving at a constant speed in east direction. After some time, it changes its direction to west. In this journey, the car has a constant speed but a variable velocity and thus have acceleration.

Conclusion:

Therefore, the car is moving at a constant speed but has acceleration.