Question Detail
Question
The acceleration with which a particle moves is given as a(t) = (-3 + 2t²) m/s². Find its velocity at time t = 3s, given that the velocity at t = 0 is zero.
Correct Answer
Option C 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. Using v(0)=0, we find C=0. Then v(3) = -3(3) + (2/3)(27) = -9 + 18 = 9 m/s.
Hint
Integrate the acceleration function with respect to time and use the initial condition to find the constant of integration.