Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t³, where t is in seconds. When it momentarily stops its acceleration is: A) 0 B) -73 m/s² C) -30 m/s² D) -9.8 m/s² E) 9.2* 10³ m/s²

Question

Quizplus · Accepted Answer

The object momentarily stops when its velocity is zero. The velocity is the first derivative of x(t): v(t) = 75 - 3t^2. Setting v(t) = 0 gives t = 5 seconds. The acceleration is the second derivative of x(t): a(t) = -6t. At t = 5 seconds, a(t) = -30 m/s².

Starting at Time T = 0, an Object Moves Along