A partical moves along a straight line such that its displacement `s=alphat^(3)+betat^(2)+gamma`, where t is time and `alpha`, `beta` and `gamma` are constant. Find the initial velocity and the velocity at `t=2`.

Explanation

`s=alphat^(3)+betat^(2)+gamma`
`v=(ds)/(dt)(alphat^(3))+d/(dt)(betat^(2))+d/(dt)(gamma)`
`=alpha.3t^(2)+beta.2t+0`
`=3alphat^(2)+2betat`
For initial quantities, use time t=0
Initial velocity `=3alpha(0)+2beta(0)=0`
A`t t=2`,
` v=3alpha(2)^(2)+2beta(2)`
`=12alpha+4beta`