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

Answer

3

Explanation

`v = (ds)/(dt) = At + Bt^(2)`
`int_(0)^(s) ds = int_(1)^(s) (At + Bt^(2)) dt`
`s = (A)/(2) |(|t^(2)|_(1)^(2)) + (B)/(3) (|t^(3)|_(1)^(2))|`
`= (A)/(2) (2^(2) - 1^(2)) + (B)/(3) (2^(3) - 1^(3))`
`= (3 A)/(2) + (7 B)/(3)`