Question

A particle moves according to the equation `s=1-1/t^2`, how do you find its acceleration?

Answer 1

Assuming `s` is the position function, recall that acceleration is the second derivative of position. Therefore, take two derivatives in a row to obtain the acceleration.

The first derivative gives you velocity, and the second gives you acceleration.

`(ds)/(dt) = vecv = 2/t^3`

`color(blue)(veca) = (d^2s)/(dt^2) = d/(dt)[(ds)/(dt)] = d/(dt)[2/t^3] = color(blue)(-6/t^4)`

What acceleration does the particle have after `"3 s"` have passed? Is it slowing down or speeding up?