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 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

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Quizplus · Accepted Answer

The instantaneous acceleration is the derivative of the velocity function. Differentiating v(t) = 2.00 + 3.00t - 1.0t^2 gives a(t) = 3.00 - 2.0t. Substituting t = 4.00 s, a(4.00) = 3.00 - 2.0(4.00) = -5.00 m/s².

The Velocity of an Object as a Function of Time