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

Answer

a

Explanation

`v=At+Bt^(2)`
`(dx)/(dt)=At+Bt^(2)`
`intdx=int_(t=1)^(t=2)(At+Bt^(2))dt`
`=A((t^(2))/(2))_(1)^(2)+B((t^(3))/(3))_(1)^(2)`
`=(3A)/(2)+(7B)/(3)`