Question

Which one of the following statements is correct?
(a) A body has a constant velocity but varying speed
(b) A body has constant speed but a varying value of the velocity
(c) A body has a constant speed and zero acceleration
(d) A body has a constant speed but velocity is zero

Answer 1

Hint: In this solution, we will use the definition of velocity, speed, and acceleration to determine the correct statement. Velocity of a body is a vector quantity that depends on the direction of the motion of the body as well on the magnitude of the speed of the body. On the other hand speed is a scalar quantity, which means it is independent of the direction of motion of the body.

Complete step by step solution:
In option (A), if a body has constant velocity, it means that the magnitude of the velocity and the direction of the velocity vector remain constant. Since speed is equal to the magnitude of the velocity vector, it will also be constant in this case hence option (A) is incorrect.
In option (B), we have been told that a body has constant speed but varying velocity. This is entirely possible as the body can move with a constant speed but can have a changing velocity due to a change in its direction. For example, a car going on a roundabout can have a constant speed but since it will have a constantly changing direction, it can have a varying velocity. Hence option (B) is correct.
In option (C), a body having constant speed can have varying acceleration is again the direction of the velocity is changing. If the direction of the velocity vector is changing, the body will have non-zero acceleration hence option (C) is also correct.
In option (D), a body with a constant speed cannot have a zero velocity since the velocity vector has a magnitude that is equal to the speed of the body. So, if the velocity is zero, the speed also has to be zero.
So, option (D) is incorrect.

Note:
An example of the situation in option (B) can also be thought of in swinging a stone tied to a string around us with constant speed. In this case, the direction of the stone will be constantly changing so its velocity will also change even if the speed of the stone will be constant.