Let the instantaneous velocity of a rocket, just after launching, be given by the expression `v=2t+3t^2` (where v is in `ms^-1` and `t` is in seconds). Find out the distance travelled by the rocket from `t=2s` to `t=3s`.

Options

A. `24m`
B. `14m`
C. `36m`
D. `20m`

Answer

A

Explanation

To find the distance travelled, we need to integrate v. [The limits of integration will be from `2s` to `3s` as we have to find the distance travelled between `t=2s` and `t=3s`.
`x=int_2^3vdt=int_2^3(2t+3t^2)dt=|(2t^2)/(2)+(3t^3)/(3)|_2^3`
`=|t^2+t^3|_2^3=24m`