Serway & Jewett — Conservation of Energy: Problem 31

As the driver steps on the gas pedal, a car of mass \(1\,160\text{ kg}\) accelerates from rest. During the first few seconds of motion, the car’s acceleration increases with time according to the expression \[ a = 1.16t - 0.210t^2 + 0.240t^3 \] where \(t\) is in seconds and \(a\) is in \(\text{m/s}^2\). (a) What is the change in kinetic energy of the car during the interval from \(t = 0\) to \(t = 2.50\text{ s}\)? (b) What is the minimum average power output of the engine over this time interval? (c) Why is the value in part (b) described as the minimum value?