The position of a particle moving along a line is given by s(t) = t^3 - 12t + 3. At what time t is the particle at rest?

Core Concept

The particle is at rest when its velocity is zero. Velocity is the derivative of position: v(t) = s'(t) = 3t^2 - 12. Set v(t) = 0: 3t^2 - 12 = 0 → 3t^2 = 12 → t^2 = 4 → t = ±2. So the particle is at rest at t = 2 and t = -2.