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+g//2+f//3`
B. `v+g+f`
C. `v+g//2+f`
D. `v+2g+3f`

Answer

a

Explanation

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