Question Detail
Question
The acceleration of a moving particle is given as a(t) = (-3 + 2t²) m/s². Find the velocity of the particle at time t = 3s, given that the velocity of the particle at t = 0 is zero.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Velocity is the integral of acceleration: v(t) = ∫ a(t) dt = ∫ (-3 + 2t²) dt = -3t + (2/3)t³ + C. At t=0, v=0 => C=0. So v(3) = -3(3) + (2/3)(27) = -9 + 18 = 9 m/s.
Hint
Integrate acceleration to get velocity. Use initial condition to find constant of integration.