Question

(a) Can a body have zero velocity and still be accelerating?
(b) Can a body have a constant speed and still have a varying velocity?
(c) Can a body have a constant velocity and still have varying speed?

Answer 1

(a)

1. Yes, an object can have zero velocity and still be accelerating simultaneously.
2. Let us consider an object moving in the forward direction.
3. Now, suddenly a force acts on it and tries to accelerate the object in the reverse direction.
4. While observing the object, you will find that the object will continue to move forward for some time and then stops instantly.
5. Then the object will start to move in the backward direction.
6. For example:-
   When the body is projected vertically up, at the highest point its speed becomes zero whereas it is accelerating downwards with $g=9.8m/s^2$.

(b)

1. Yes if the body is travelling with uniform speed in a circular track its speed remains the same but the velocity is non-uniform as the direction is changing every time.
2. One simple example is what we call Uniform Circular Motion (Uniform circular motion can be described as the motion of an object in a circle at a constant speed).
3. For example, consider a vehicle moving with a constant speed on a circular path.
4. Here, the speed is constant, but the direction of the vehicle is changing continuously.
5. As we know, velocity is a vector quantity, so as the direction of motion changes, velocity also changes.
6. 

(c)

1. No, a body can not have its velocity constant, while its speed varies.
2. Rather, it can have its speed constant and its velocity varying.
3. For example in a uniform circular motion.
4. The velocity of an object can be changed by: Change of speed, Change of direction.
5. In a uniform circular motion, the direction is not always the same, rather, it keeps changing. While the speed can remain the same.
6. So in this way, the velocity can vary and the speed can be constant. But the vice versa is never possible.