The displacement of a particle varies as `s=k/alpha(1-e^(-alphat))`, where `k` and `alpha` are constants. Find the velocity and acceleration in terms of t and their initial values.

Explanation

`s=k/alpha(1-e^(-alphat))`
`=k/alpha[1-{e^(-alphat)}]`
`v=(ds)/(dt)=k/alpha[0-e^(-alphat).(-alpha.1)]`
`=k e^(-alphat)`
`=k {e^((-alphat))}`
`a=(dv)/(dt)=k. e^(-alphat).(-alpha.1)`
`=-alpha k e^(-alphat)`
At `t=0, v=k`
and `a=-alphak`
Recall: First differentiate the outer layer, then the inner layer and then multiply the two differentials.