A particle moves with a non zero initial velocity $v_{0}$ and retardation $k v$ , where $v$ is the velocity at any time $t$ .
The particle will cover a total distance $\frac{v_{0}}{k}$
The particle comes to rest at $t = \frac{1}{k}$
Particle continues to move for long time
at time $\frac{1}{α}, v = \frac{v_{0}}{2}$

Question

A particle moves with a non zero initial velocity $v_{0}$ and retardation $k v$ , where $v$ is the velocity at any time $t$ .
The particle will cover a total distance $\frac{v_{0}}{k}$
The particle comes to rest at $t = \frac{1}{k}$
Particle continues to move for long time
at time $\frac{1}{α}, v = \frac{v_{0}}{2}$

Toppr Admin · Accepted Answer

U-v0- retardation a-kv and v is the velocity at time t-using v-u-x2212-at- we will get v-v0-x2212-kvt-x21D2-t-v0kv-x2212-1kif v-0-t-x221E- So the particle will be moved for a long time-xA0-xA0-

A particle moves with a non zero initial velocity v0 and retardation kv, where v is the velocity at any time t.The particle will cover a total distance v0kThe particle comes to rest at t=1kParticle continues to move for long timeat time 1α,v=v02

u=v0, retardation a=kv and v is the velocity at time t.using v=u−at, we will get v=v0−kvt⇒t=v0kv−1kif v=0,t=∞. So the particle will be moved for a long time.

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