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. (a)
B. (b)
C. (C )
D. (d)

Answer

B

Explanation

Accelertion, ` A= F/M = F_0/me^(-bt)`
or ` (dv)/(dt) = F_0/m e^(-bt)` or ` d v = F_0/m e^(bt) dt`
get ` int _0^v d v = int F_0/m e^(- bt) dt`
or ` v = F_0/m [ - 1/b e ^(bt) ]_0^t = - F_0 /(mb) [e^(-t) - 1 ]`
`= F_0/(mb) [1 - e^(bt) ]`
When ` t=0`, v=0` and when ` t = prop , v= F_0/9mb)`
thus velocity increases continuously and attains maximum value`, v= F_0/(mb) at ` t= prop`. Thus, option
` (b) is true.