The velocity of 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//3) `
B. ` v_0 +g+f`
C. ` v_0(g//2)+f`
D. ` v_0+2g +3f`

Answer

A

Explanation

we are given velocity ` v= v_0 +g t +ft^(2) " " therefore " " v =(dx)/(dt) " "or int _0^(x) dx = int _0^(t) vdt `
`x= int _0^(t) (v_0_g t +ft ^(2)) dt or " " x=v_0 t+ (g t^(2))/(2) + ( ft^(2))/(3) : At t = 1 sec , x = v_0 +( g)/(2) +(f)/(3) `