Question Detail
Question
Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. At the end of 1.0 s the acceleration of the auto is:
Correct Answer
Option D is the correct answer.
Detailed Explanation
Velocity v(t) = dx/dt = 27 - 12t². Acceleration a(t) = dv/dt = -24t. At t=1 s, a(1) = -24 × 1 = -24 m/s².
Hint
Acceleration is the second derivative of position with respect to time.