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

1 Answer
Jan 11, 2017

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?