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

`underset(0)overset(x)int dx = underset(0)overset(1)int vt = underset(0)overset(1)int (v_(0) + g t + f t^(2)) dt`
`x = [v_(0)t + (g t^(2))/(2) + (f t^(3))/(3)]_(0)^(1)`
`x = (v_(0) + (g)/(2) + (f)/(3))`