Question

if `a=3t^(2)+2t`, initial velocity is `5 m//s`. Find the velocity at t=4s. The motion is in straight line, a is acceleration in `m//s^(2)` and t is time in seconds.

Answer 1

`a=(dv)/(dt)=3t^(2)+2t`
`int_(5)^(v) dv=int_(0)^(4)(3t^(2)+2t)dt`
`|v|_(5)^(v)=3t^(3)/3+2t^(2)/2=|t^(3)+t^(2)|_(0)^(4)`
`v-5={(4)^(3)+(4)^(2)}-{0}`
`v=85 m//s`