Question

A partical is moving in a straight line such that its displacement at any time t is given by `s=4t^(3)+3t^(2)`. Find the velocity and acceleration in terms of t.

Answer 1

`s=4t^(3)+3t^(2)`
`v=(ds)/(dt)=d/(dt)(4t^(3))+d/(dt)(3t_(2))`
`=4.3t^(3-1)+3.2t^(2-1)`
`=12t^(2)+6t`
`a=(dv)/(dt)=d/(dt)(12t^(2))+d/(dt)(6t)`
`=12.2t^(2-1)+6.t^(1-1)`
`=24t+6 `