Question

Mark the correct statements for a particle going on a straight line :
(a) If the velocity and acceleration have opposite sign, the object is slowing down.
(b) If the position and velocity have opposite sign, the particle is moving towards the origin.
(c) If the velocity is zero at an instant, the acceleration should also be zero at that instant.
(d) If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

Answer 1

(a) If the velocity and acceleration have opposite sign, the object is slowing down.

(b) If the position and velocity have opposite sign, the particle is moving towards the origin.

(d) If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

Explanation:

If the acceleration and velocity of the particle has opposite sign it has a retarding effect. As is the case of a particle thrown vertically upward. So (a) is true.

(b) is also obviously true.

(c) is not true. Consider the case of a particle thrown vertically upward. At its highest point the velocity is zero but acceleration is not zero. Acceleration is defined as rate of change of velocity. If in a time interval velocity is zero, it means in this interval velocity does not change. So acceleration at any instant in this time interval is zero. Hence (d) is true.