A particle moving along x-axis has acceleration `f`, at time `t`, given by `f = f_0 (1 - (t)/(T))`, where `f_0` and `T` are constant.
The particle at `t = 0` has zero velocity. In the time interval between `t = 0` and the instant when `f = 0`, the particle's velocity `(v_x)` is :

Options

A. `(1)/(2) f_(0)T^(2)`
B. `f_(0)T^(2)`
C. `(1)/(2) f_(0)T`
D. `f_(0)T`

Answer

C

Explanation

`f = f_(0) (1 - (t)/(T))`
`f` will be zero at `t = T`.
`(dv)/(dt) = f_(0) (1 - (t)/(T))`
`int dv = int f_(0) (1 - (t)/(T)) dt`
`v = f_(0) (t - (t^(2))/(2T))`
At `t = T, v = f_(0) (T - (T^(2))/(2T)) = (f_(0)T)/(2)`