A particle moves in a straight line with an acceleration `a ms^-2` at time 't' seconds where `a = - (1)/(t^2)` When `t = 1` the particle has a velocity of `3 ms^-1`. Find the velocity of the particle at `t = 4 s`.

Options

A. `5.25 m//s`
B. `1.25 m//s`
C. `2.25 m//s`
D. `8.25 m//s`

Answer

C

Explanation

`a = (dv)/(dt) = (-1)/(t^2) rArr = underset(3)overset(v)(int) dv = - underset(1)overset(4)(int) (1)/(t^2) dt`
`rArr v - 3 = [(1)/(t)]^4 = (1)/(4) - 1`
`rArr v = 3 - (3)/(4) = (9)/(4) = 2.25 m//s`.