The velocity of a particle is `v = v_(0) + g t + ft^(2)`. If its position is ` x=0 ` at ` t= 0 `, then its displacement after unit time `( t = 1 )` is

Options

A. `v_(0) + g//2 + f`
B. `v_(0) + 2g + 3f`
C. `v_(0) + g//2 + f//3`
D. `v_(0) + g+ f`

Answer

C

Explanation

We know that, `v= (dx)/(dt) rArr dx= v dt`
Integrating, `underset(0)overset(x)int dx= underset(0)overset(t)int v dt`
or `x= underset(0)overset(t)int (v_(0) + g t + ft^(2))dt or, x = v_(0)t + (g t^(2))/(2) + (ft^(3))/(3)`
At t= 1, `x= v_(0) + (g)/(2) + (f)/(2)`