The velocity of a particle is `v = v_(0) + gt + 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) + g//2 + 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 , `int _(0)^(x) dx = int _(0)^(t) v dt `
or` x = int _(0)^(t) ( v_(0) + gt + ft^(2)) dt = [ v_(0)t (gt^(2)/(2) + (ft^(3)/(3) ]_(0)^(t) `
or, ` x = v_(0)t + (gt^(2))/(2) + (ft^(3))/(3) `
At ` t= 1, x = 0 v_(0) + (g)/(2) + (f)/(3)`.