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# Answer to Question #6352 in Mechanics | Relativity for Jessica

Question #6352
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?
1
2012-02-09T08:20:20-0500
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.

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Assignment Expert
20.06.13, 15:03

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.

Philo
20.06.13, 01:32

But the friction force is supposed to be negative