A particle moves along a straight line with equation of motion s = f (t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 3.

f (t) = (t ^-1) - t

F (t) = (t^-1) - t

Taking derivative:

f' (t) = d/dt (t^-1) - t) = d/dt (t^-1) - d/dt (t)

f' (t) = - 1 (t^-2) - 1

= - t^-2 - 1

f' (t) = v (t),

It can be also written as:

-1/t^2 - 1

So v (3) = - 1 / (3^2) - 1 = - 1/9 - 1 = - 10/9