Question

What is the instantaneous velocity of an object with position at time t equal to `f(t)= (sqrt(t^3-3t),tsqrt(t^2-2))` at `t=3`?

Answer 1

`(3.182,6.047)`

Explanation:

Since velocity is defined as rate of change in position, the velocity function may be given as the derivative of the position function with respect to time.
Hence, by using the power rule in conjunction with the product rule we get

`therefore v(t)=dx/dt=f'(t)=((3t^2)/(2sqrt((t^3-3t))), t^2/(sqrt(t^2-2))+sqrt(t^2-2))`

`therefore v(3)=(27/(2sqrt(18)),9/sqrt7+sqrt7)`

`=(3.182,6.047)`