Question Detail
Question
A particle starts from rest and has an acceleration given by a(t) = 4t m/s². What is its velocity as a function of time?
Correct Answer
Option C is the correct answer.
Detailed Explanation
Velocity is the integral of acceleration with respect to time. v(t) = ∫ a(t) dt = ∫ 4t dt = 2t² + C. Since the particle starts from rest, the initial velocity v(0) = 0, so the constant of integration C = 0. Therefore, v(t) = 2t² m/s.
Hint
Recall that velocity is the antiderivative (integral) of acceleration. Remember to account for the initial condition (starts from rest).