Question

A particle of mass `m` is at rest the origin at time ` t= 0 ` . It is subjected to a force ` F(t) = F_(0) e^(-bt)` in the `x` - direction. Its speed ` v(t)` is depicted by which of the following curves ?
A.
B.
C.
D.

Answer 1

Correct Answer - B
Given that `F(t) = F _(0) e ^(-bt) rArr (m (dv))/ (dt) = F_(0) e^(-bt)`
` (dv) /(dt) = F_(0) / (m) e ^(-bt) rArr int _(0)^(v) (dv) = (F_(0))/(m) int _(0)^(t) e ^(-bt) dt `
` v = (F_(0))/(m) [ (e^(-bt))/ (-b) ]_(0)^(t) = (F_(0))/(m) [ -( e^(-bt) - e^(-0))]`
rArr ` v = (F_(0))/(mb)[ 1 - e^(-bt)]`