Question

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

Answer 1

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