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 = 4.00 s. A)-2.00 m/s² B)-5.00 m/s² C)1.00 m/s² D)0.00 m/s² E)-1.00 m/s²

Question

Quizplus · Accepted Answer

The instantaneous 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/s^2)t
At t = 4.00 s, 
a(4.00 s) = 3.00 m/s - 2(1.0 m/s^2)(4.00 s) = -5.00 m/s^2
Therefore, the best choice is B which represents the unit of instantaneous acceleration at t = 4.00 s.

The Velocity of an Object as a Function of Time