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

Answer

B

Explanation

`v=(dx)/(dt)=v_(0)+g t+ft^(2)`
`int_(0)^(x) dx=int_(0)^(1)(v_(0)+g t+ft^(2))dt`
`x=|v_(0)t+(g t^(2))/2+(f t^(3))/3|_(0)^(1)`
`=v_(0)+g/2+f/3`