Question

A radius vector of a particle varies with time t as r = at $(1-\alpha t)$, Where $\alpha$ is a constant vector and $\alpha$ is a positive constant.Find the distance covered before the particle comes to rest

Answer 1

It is given that

$r=at(1-\alpha t)=at-\alpha a{t}^2$

$v=\frac{dr}{dt}=a-2ta\alpha$

$accelaration,a=\frac{dv}{dt}=-2\alpha a$

Using second equation of motion

$s=ut+\frac{1}{2}a{t}^2$

$s=-\alpha a{t}^2$ (initial velocity u = 0)