Question

The displacement $x$ (in meter) of a particle of mass $m$ (in kg) moving in one dimension under the action of a force, is related to time $t$ (in sec) when its velocity is zero, will be

Answer 1

$a=\frac{F}{m}$

$⟹\frac{dv}{dt}=\frac{F}{m}$

$⟹dv=\frac{F}{m}dt$

Integrating-

$v-u=\frac{F}{m}t$

$⟹v=\frac{dx}{dt}=u+\frac{F}{m}t$

$⟹dx=udt+\frac{F}{m}tdt$

$⟹x=ut+\frac{F}{2m}{t}^2$