The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 5.00 s. A) -8.00 m/s² B) -7.00 m/s² C) 2.00 m/s² D) 0.00 m/s² E) -2.00 m/s²

Question

Quizplus · Accepted Answer

The instantaneous acceleration can be found by taking the derivative of the velocity function with respect to time: a(t) = dv/dt = 3.00 m/s - 2(1.0 m/s²) t At time t = 5.00 s, we have: a(5.00) = 3.00 m/s - 2(1.0 m/s²) (5.00 s) a(5.00) = 3.00 m/s - 10.00 m/s² a(5.00) = -7.00 m/s² Therefore, the instantaneous acceleration at time t = 5.00 s is -7.00 m/s², which corresponds to choice B.

The Velocity of an Object as a Function of Time