Question

A particle initially at rest is subjected to two forces. One is constant, the other is a retarding force proportion at to the particle velocity. In the subsequent motion of the particle.

• A. The acceleration will increase from zero to a constant value.
• B. The acceleration will decrease from its initial value to a zero.
• C. The velocity will increase from zero to a maximum & then decrease.
• D. The velocity will increase from zero to a constant value.

Answer 1

The correct option is B The acceleration will decrease from its initial value to a zero.

Let,

Constant force $=K_1$

Variable force $=-K_{2}V$

Net Force $F=K_1-K_{2}V$

Acceleration $a=\frac{K_1-K_{2}V}{m}$

As the velocity increases the net force will decrease. When both retarding and constant forces become equal then net force is zero. Hence the velocity is maximum and acceleration will increase from zero to constant.