Suppose the position an object moving in a straight line is

Suppose the position an object moving in a straight line is given by s(t) = 3t3 - 8t2 + 6. Find the instantaneous velocity when t = 4. The instantaneous velocity is at t = 4. (Simplify your answer.)

Solution

Velocity is the first derivative of the position function, so to find the answer, one must find the derivative of the function and then plug in the time for the instantaneous velocity.

s(t) =3t^3 - 8t^2 +6
s\'(t) = 9t^2 - 16t
s\'(4) = 3(4)^2 - 2(4)
= 40