A car with a mass of 1.50x10^3 kg starts from rest and accelerates to a speed of 18.0 m/s in 12.0s. Assume that the force of resistance constant at 400.0 N during this time. What is the average power developed by the car's engine?
From the equation for speed V = a*t let's find car's acceleration: a = V/t. Using the Newton's Second Law: F - Fres = ma, where Fres is the force of resistance (Fres = 400 N), F - force of engine. So, F = Fres + ma. Average power can be found from the equations for total engine's work: A = F*S = P*t, P = F*S/t. S can be found from the equation of displacement: S = (a*t^2)/2. So, P = (Fres + m*V/t)*(V/t*t^2)/(2t) = (Fres + m*V/t)*V/2 = (400+1500*18/12)*18/2 = 23850 W.
It is negative, the sign here means direction. We have F-Fres=ma, so F and Fres have opposite directions, F is collinear with direction of the car motion, Fres is opposite to it. The magnitude of Fres is positive, that's right, but when construction equations we keep in mind that it's directed opposite to the motion of the car.