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

1 Answer
Truong-Son N.
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?

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