Read each statement below carefully and state with reasons and examples, if it is true or false ;
A particle in one-dimensional motion
with zero speed at an instant may have non-zero acceleration at that instant
with zero speed may have non-zero velocity,
with constant speed must have zero acceleration,
with positive value of acceleration must be speeding up.

Question

A particle moves in a circle of radius 2 m with a speed of 6 m/s. What is the centripetal acceleration of the particle?

Answer 1

(a) A particle in one-dimensional motion with zero speed at an instant may have non-zero acceleration at that instant

True.

Speed can be zero at an instant while acceleration is non-zero.

Example:

Consider a ball thrown vertically upward.
At the highest point of its motion, the instantaneous speed of the ball is zero.

However, the acceleration due to gravity acting on the ball is still present and has a constant value:

a = g (downward)

Thus, a particle can have zero speed but non-zero acceleration at the same instant.

(b) A particle in one-dimensional motion with zero speed may have non-zero velocity

False.

Speed is the magnitude of velocity.

If the speed of a particle is zero, then the magnitude of its velocity is zero.

Therefore, the velocity itself must also be zero.

(c) A particle in one-dimensional motion with constant speed must have zero acceleration

True.

In one-dimensional motion, constant speed implies that both the magnitude and direction of velocity remain unchanged.

Since acceleration is the rate of change of velocity, no change in velocity means:

Acceleration = 0

Hence, in one-dimensional motion, constant speed requires zero acceleration.

(d) A particle in one-dimensional motion with positive value of acceleration must be speeding up

False.

Acceleration being positive only indicates its direction, not whether the particle is speeding up or slowing down.

If the velocity of the particle is negative and acceleration is positive, the particle slows down.

Example:

A particle moving to the left (negative velocity) with acceleration acting to the right (positive acceleration) will slow down.

Thus, a positive acceleration does not necessarily mean that the particle is speeding up.

Summary:

Solution and Explanation