A car (mass 920 kg) drives up a hill (height 328 m) in 143 seconds. At the bottom of the hill, it has a speed of 24 m/s, but at the top, it has slowed down to 14 m/s. Neglecting friction, what is the average engine power?
I tried using 1/2mv^2 and it didn't work.
To find the average engine power, we need to calculate the work done by the car to overcome the gravitational potential energy and change in kinetic energy.
Step 1: Calculate the gravitational potential energy (GPE)
The gravitational potential energy is given by the formula:
GPE = mgh
Where:
m = mass of the car = 920 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the hill = 328 m
Plugging in the values:
GPE = (920 kg) x (9.8 m/s^2) x (328 m)
GPE = 2,935,168 J (Joules)
Step 2: Calculate the change in kinetic energy (ΔKE)
Since the car slows down from 24 m/s to 14 m/s, the change in kinetic energy is given by the formula:
ΔKE = (1/2)mvf^2 - (1/2)mvi^2
Where:
m = mass of the car = 920 kg
vi = initial velocity = 24 m/s
vf = final velocity = 14 m/s
Plugging in the values:
ΔKE = (1/2)(920 kg)(14 m/s)^2 - (1/2)(920 kg)(24 m/s)^2
ΔKE = -207,680 J (Since the change is negative, indicating a decrease in kinetic energy)
Step 3: Calculate the total work done
The total work done is the sum of the work done to overcome the gravitational potential energy and the change in kinetic energy:
Total work done = GPE + ΔKE
Total work done = 2,935,168 J + (-207,680 J)
Total work done = 2,727,488 J
Step 4: Calculate the time taken (t)
The time taken to drive up the hill is given as 143 seconds.
Step 5: Calculate the average power
The average power is given by the formula:
Power = Work done / Time taken
Plugging in the values:
Power = 2,727,488 J / 143 s
Power ≈ 19,058.67 W (Watts)
Therefore, the average engine power of the car is approximately 19,058.67 Watts.