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The position function of a car moving along a mountain road is given by the function f(t) = t3 - 2t2 + 4 kilometers, where t is in hours. What is the instantaneous velocity of the car at t = 2 hours?

A.
3.00 km/hr
B.
4.00 km/hr
C.
4.41 km/hr
D.
5.21 km/hr

User LongNV
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1 Answer

4 votes

Final answer:

The instantaneous velocity of the car at t = 2 hours is 4 km/hr.

Step-by-step explanation:

To find the instantaneous velocity of the car at t = 2 hours, we need to differentiate the position function f(t) = t^3 - 2t^2 + 4 with respect to time. Taking the derivative, we get f'(t) = 3t^2 - 4t. Plugging in t = 2 into the derivative, we get f'(2) = 3(2)^2 - 4(2) = 12 - 8 = 4 km/hr.

User Manuel G
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8.1k points