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 m/s² B)-73 m/s² C)-30 m/s² D)-9.8 m/s² E)9.2 x 10³ m/s²

Question

Quizplus · Accepted Answer

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

Starting at Time T = 0, an Object Moves Along