A particle is moving with velocity `v=4t^(3)+3 t^(2)-1 m//s`.
The displacement of particle in time `t=1 s` to `t=2 s` will be

Options

A. 21 m
B. 17 m
C. 13 m
D. 9 m

Answer

A

Explanation

`v=(ds)/(dt)=4t^(3)+3t^(2)-1`
`int_(0)^(s) ds=int_(1)^(2)(4t^(3)+3t^(2)-1)dt`
`s=|t^(4)+t^(3)-t|_(1)^(2)`
=`{(2)^(4)+(2)^(3)-(2)}-{(1)^(4)+(1)^(3)-(1)}`
`=22-1=21 m`