Question

A particle moving with a velocity u is subjected to a retarding force as a result of which it decelerates at a rate a=-k√v where v is the instantaneous velocity and is the positive constant.Time taken by the particle to come to rest is given by

Answer 1

let a is magnitude ofthe deceleration .
and v is the speed of particle .

a/c to question,
a =K√v { where K is the constant

dv/dt =K√v

dv/√v = K.dt

integrate both sides ,
[ 2√v ] = K [ t ] put the limit

2[ √v - √vo ] = Kt

t=2[√v-√vo]/K