Question

A particle moves with a non zero initial velocity $v_0$ and retardation $kv$, where $v$ is the velocity at any time $t$.

• A. The particle will cover a total distance $\frac{v_0}{k}$
• B. The particle comes to rest at $t=\frac{1}{k}$
• C. Particle continues to move for long time
• D. at time $\frac{1}{\alpha },v=\frac{v_0}{2}$

Answer 1

The correct option is C Particle continues to move for long time

$u=v_0,$ retardation $a=kv$ and $v$ is the velocity at time $t$.
using $v=u-at,$ we will get $v=v_0-kvt\Rightarrow t=\frac{v_0}{kv}-\frac{1}{k}$
if $v=0,t=\infty$. So the particle will be moved for a long time.