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?
To find the average engine power, we need to calculate the work done by the engine and divide it by the time taken.
First, let's find the work done by the engine. The work is equal to the change in potential energy of the car.
The potential energy of an object is given by the formula:
Potential Energy = mass * gravity * height
Where:
- mass is the mass of the car (920 kg)
- gravity is the acceleration due to gravity, which we'll assume to be 9.8 m/s²
- height is the height of the hill (328 m)
Potential Energy = 920 kg * 9.8 m/s² * 328 m
Potential Energy = 2,858,112 Joules
Since the car slows down as it gains height, the work is negative. Therefore, the work done by the engine is -2,858,112 Joules.
Next, let's calculate the average engine power. Power is defined as work done divided by time taken:
Power = Work / Time
- Work is -2,858,112 Joules (negative because it's work done against gravity)
- Time taken is 143 seconds
Power = -2,858,112 Joules / 143 seconds
Power = -19,994.52 Watts
However, the negative sign represents that the power is being supplied by the engine, not dissipated. Therefore, the average engine power is approximately 19,994.52 Watts.