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

B

Explanation

`F(t ) = F_0 E^(-bt ) `(given )
Acceleration `a=(F)/(m ) = (F_0)/(m) e ^(-bt) or ( dv )/(dt) = (f_0)/(m) e^(-bt) or dv = (F_0) /(m ) e^(-bt) or dv = (F_0)/(m) e^(-bt) dt `
integrating both sides , we get
` int_(0) ^(v) dv = int_(0)^(t) (F_0)/(m) e^(-bt) dt , v = (F_0)/(m) [ (e^(-bt))/(-b)]=(F_0)/(mb) [1-e^(-bt)]`
when `t=0` , v=0 and when ` t = oo , v =(F_0)/(mb)`
thus , option (b ) represents the corrrect graph .