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: A)23 m/s² B)15 m/s² C)-4.0 m/s² D)-12 m/s² E)-24 m/s²

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Quizplus · Accepted Answer

The acceleration is the second derivative of the position function x(t). Differentiating x(t) = 27t - 4.0t^3 twice gives a(t) = -24t. At t = 1.0 s, a(1) = -24(1) = -24 m/s².

Over a Short Interval near Time T = 0 the Coordinate