Question

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?

Answer 1

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.