The position of a particle moving along the x-axis is given by x(t) = 3t² - 2t + 5, where x is in meters and t is in seconds. What is the acceleration of the particle at t = 2 s?

Core Concept

Acceleration is the second derivative of position with respect to time. The velocity is v(t) = dx/dt = 6t - 2. The acceleration is a(t) = dv/dt = 6 m/s². Since acceleration is constant, it is 6 m/s² at all times, including t = 2 s. Option A is incorrect because the acceleration is not zero. Option B is the velocity at t = 0 s, not the acceleration. Option D would be the result if we incorrectly took the third derivative of position.