Question

!calculus!

The position function of a car moving along a mountain road is given by the function f(t) = t^3 - 2t^2 + 4 kilometers, where t is in hours. What is the instantaneous velocity of the car at t = 2 hours?

Answer 1

Answer: 4 Kilometers per hour.

Explanation: The instantaneous velocity of the car at t = 2 hours can be found by taking the first derivative of the position function. The derivative of f(t) = t^3 - 2t^2 + 4 is f'(t) = 3t^2 - 4t.

Substituting t = 2 into the derivative function gives us:

f'(2) = 3 * 2^2 - 4 * 2 = 12 - 8 = 4

So, the instantaneous velocity of the car at t = 2 hours is 4 kilometers per hour.