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 ?

Options

A.
B.
C.
D.

Answer

C

Explanation

`F(t) = F_(0)e^(-bt) rArr ma = F_(0)e^(-bt)`
`rArr dv = (F_(0))/(m) e^(-bt) dt`
`v = int_(0)^(1) =(F_(0))/(m) e^(-bt) dt= [(F_(0))/(mb) e^(-bt)]_(0)^(t)`
` = (-F_(0))/(mb)[e^(-bt) - 1]`
` = (F_(0))/(mb) (1-e^(-bt))`