The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? A) 18.0 m/s B) 54.0 m/s C) 0.00 m/s D) 15.0 m/s E) 108 m/s

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Quizplus · Accepted Answer

The velocity is the integral of acceleration with respect to time. Integrating a(t) = (3.00 m/s³)t from 0 to 6 s gives v(t) = (3.00/2)t². Evaluating at t = 6 s gives v(6) = (3.00/2)(6)² = 54.0 m/s.

The Acceleration of an Object as a Function of Time