As the driver steps on the gas pedal, a car of mass 1 120 kg accelerates from re
ID: 2174075 • Letter: A
Question
As the driver steps on the gas pedal, a car of mass 1 120 kg accelerates from rest. During the first few seconds of motion, the car's acceleration increases with time according to the expression below, where t is in seconds and a is in m/s2.a = 1.10 t - 0.210 t2 + 0.240 t3
(a) What is the change in kinetic energy of the car during the interval from t = 0 to t = 3.40 s?
J
(b) What is the minimum average power output of the engine over this time interval?
W
(c) Why is the value in part (b) described as the minimum value?
Explanation / Answer
1) dW = F*dx = m*a*dx With a given as a function of t and knowing Vi = 0, 2) v = ?a*dt = dx/dt ? dx = v*dt = ?a*dt*dt Performing this integration and substituting in (1), dW = m*a*v*dt = m*[1.16t-.21t²+.24t³]*[.58t²-.07t³+.06t^…? Multiplying and substituting 3 for t, I got (a) W3 = 36892 J Differentiating wrt t and setting t = 3, (b) P3 = 129 kW
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