If the velocity of a particle is `v = At + Bt^2`, where `A` and `B` are constant, then the distance travelled by it between `1 s` and `2 s` is :

Options

A. `3/2A + 4B`
B. 3A + 7B
C. `3/2A + 7/3B`
D. `A/2 + B/3`

Answer

C

Explanation

`V = At + Bt^2 rArr (dx)/(dt) = At + Bt^2`
`rArr int_0^x dx = int_1^2 (At+Bt^2) dt = [(At^2)/(2) + (Bt^3)/(3) ]_1^2`
`rArr x = (3A)/(2) + (7B)/(3)`