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 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

Here `v=v_0`+gt+`ft^(2)`
or `(dx)/(dt)=v_0`+gt+`ft^(2)`
`dx=v_0dt`+ gt dt+`ft^2` dt
`int_(0)^(x) dx=v_(0)int_(0)^(1)dt+gin_(0)^(1)t dt +f int_(0)^(1) t^(2) dt`
`=v_0 +(g)/(2)+(f)/(3)`