Question Detail
Question
A car's position as a function of time is given by x(t) = 5t² + 2t, where x is in meters and t is in seconds. What is the instantaneous velocity of the car at t = 2 s?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Instantaneous velocity v(t) is the time derivative of the position function x(t). v(t) = dx/dt = d(5t² + 2t)/dt = 10t + 2. At t = 2 s, v(2) = 10(2) + 2 = 20 + 2 = 22 m/s.
Hint
Instantaneous velocity is found by taking the derivative of the position function with respect to time.