Question

Can a body have zero velocity and still be accelerating? Give examples.

Answer 1

Hint Acceleration is defined as the rate of change of velocity of an object with respect to time. Whenever there is a change in velocity, the object undergoes an acceleration. So, whenever the magnitude or the direction of the velocity changes, there is a non-zero value of acceleration corresponding to it.

Step by step solution
Acceleration is the rate of change of velocity of an object with respect to the time over which this change occurs. It is possible to have a non-zero value of acceleration when the velocity of a body is zero.
This can happen when it goes in a particular direction, and a force which acts in a direction opposite to it, acts upon it. Due to this force, the velocity of the object starts decreasing and continues to decrease until it reaches zero. After this, the object starts moving in the opposite direction (that is in the direction of force). At the point where the velocity becomes zero, only the instantaneous velocity of the body is zero, at any time before or after this time, the object has a non-zero velocity.
This means that the change in the velocity is still taking place when the velocity of the object reaches zero. Therefore, the body is still accelerating.
Example- When a ball is thrown upwards on earth with a constant velocity, the gravitational force of the earth acts on it in the opposite direction. At the highest point, the velocity of the ball becomes zero, after which it starts to fall down. At this point, the velocity of the ball is zero yet its acceleration is equal to $g = 9.8m/{s^2}$.
This property can also be observed in a Simple harmonic motion of a spring or a pendulum. When the maximum displacement is reached, the restoring force takes over and the object starts to accelerate in the opposite direction. At this point too, the velocity of the object is zero but it has some value of acceleration corresponding to the restoring force.

Note This case where the velocity decreases continuously, becomes zero and then increases in the opposite direction indicates that a force is acting in a direction opposite to the motion of the object. The point where the object acquires zero velocity is the point where it has the maximum potential energy.