If a car travels at a constant velocity of 70 miles/hour and exerts a force of 3000 newtons, what is the power of the car engine?

To determine the power of the car engine, we can make use of the equation:

Power = Force × Velocity

Given:

- Velocity of the car = 70 miles/hour
- Force exerted by the car engine = 3000 newtons

However, there is a unit mismatch. Velocity is given in miles/hour while force is given in newtons. We need to convert the velocity to meters per second (m/s) since the SI unit for force is the newton.

1 mile = 1.609344 kilometers
1 kilometer = 1000 meters

Therefore,

70 miles/hour = (70 miles/hour) × (1.60934 kilometers/mile) × (1000 meters/kilometer) × (1 hour/3600 seconds)

After conversion, we will have the velocity in meters per second (m/s). Once we have the units matched, we can plug in the values into the power equation to calculate the power of the car engine.

To find the power of the car engine, we can use the equation:

Power = Force × Velocity

First, let's convert the velocity from miles/hour to meters/second, since the unit of force is Newtons (which is based on the metric system). 1 mile = 1609.34 meters and 1 hour = 3600 seconds, so:

70 miles/hour = (70 × 1609.34 meters) / (1 hour × 3600 seconds)
= 31.292 meters/second (approx)

Now we can plug in the values into the equation:

Power = Force × Velocity
= 3000 newtons × 31.292 meters/second
≈ 93,876 watts

Therefore, the power of the car engine is approximately 93,876 watts.