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

Answer

C

Explanation

Here , velocity, ` v= (dx)/(dt) = A t + B t^2`
or ` dx = (A t+ Bt^2) dt` ltbRgt :. ` x= int_1^2 ( At + B T^2 ) dt = [ (A t^2)/2 + (Bt_3)/3 }_1^2`
`= A/2 (4 - 1) + B/3 (8 -1) = ( 3 A)/ 2 + 7/3 B`.