The position of a particle moving along a line is given by s(t) = t^3 - 6t^2 + 9t, where t is time in seconds and s is in meters. What is the velocity of the particle when its acceleration is zero?

Core Concept

First, find the velocity function by taking the derivative of position: v(t) = s'(t) = 3t^2 - 12t + 9. Next, find the acceleration function by taking the derivative of velocity: a(t) = v'(t) = 6t - 12. Set acceleration equal to zero: 6t - 12 = 0, so t = 2 seconds. Now find the velocity at t = 2: v(2) = 3(2)^2 - 12(2) + 9 = 12 - 24 + 9 = -3 m/s. The correct answer is C) -3 m/s.