The position function of a particle moving along a straight line is given by s(t) = t³ - 6t² + 9t, where t is measured in seconds and s is measured in meters. What is the instantaneous velocity of the particle at t = 2 seconds?

Core Concept

The instantaneous velocity is the derivative of the position function. v(t) = s'(t) = 3t² - 12t + 9. At t = 2, v(2) = 3(2)² - 12(2) + 9 = 12 - 24 + 9 = -3 m/s. Option A is incorrect because it's the negative of the correct value. Option B is incorrect because it's the velocity at t = 1 or t = 3, not t = 2. Option D is incorrect because it's the acceleration at t = 2, not the velocity.