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 acceleration is given by the derivative of velocity with respect to time:

a(t) = dv(t)/dt = 3.00 m/s - 2(1.0 m/s²) t

At t = 5.00 s:

a(5.00 s) = 3.00 m/s - 2(1.0 m/s²)(5.00 s) = -7.00 m/s²

Therefore, the best choice is B: -7.00 m/s².

The Velocity of an Object as a Function of Time