A particle of mass m is at rest at 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

D

Explanation

`F(t) = F_(0)e^(-bt)`
`m(dv)/(dt) = F_(0)e^(-bt)`
`intdv = int_(t=0)^(t=t)(F_(0))/(m) e ^(-bt)dt`
`v = (F_(0))/(mb) [e^(-bt)] + C` At `t = 0, v(t) = 0`
`0 = (-F_(0))/(mb) + C rArr C = (F_(0))/(mb)`
`v(t) = (-F_(o))/(mb) e^(-bt) + (F_(0))/(mb)`
`v(t) = (F_(0))/(mb) (1-e^(-bt))`