How much power does the engine have?

Question

A 1.50x10^3 kg car can go from 0.0km/h to 120.0 km/h in 5.8 seconds. If the average air resistance is 3.00x10^2 N, how much power does the engine have?

Answer 1

We actually have two problems. One is computing power required to accelerate the car and the other how much power is required to overcome air resistance.

Power P is a rate of flow of energy and is also a product of force F applied to maintain speed v.

P= Fv
So the power to overcome air resistance [using 3.6 km/h=m/s ]
P=Fv= 3.00E+2 x (120 x3.6)
P=1.30E+5W
since 1 hp is 746 watts
P=174hp

Now for acceleration
a= (v2-v1)/(t2-t1)
F=ma
Since power is energy floww
P=E/t
Energy = work done=force times the didstance
E=Fs
s=0.5at^2
P=[m a 0.5at^2]/t
P= 0.5m a^2 t
P=0.5m [(v2-v1)/t] ^2 t
P=0.5m [(v2-v1)] ^2 / t
P=0.5 x 1.50E+3 [(120x 3.6 -0)] ^2 / 5.8
P=24.1E+6W [ 32,305 hp!]