Final answer:
The force exerted by a 150 kg car engine that develops 500 W per kg while moving at a speed of 20 m/s is 3,750 newtons. The force is calculated using the equation P = F × v, rearranged as F = P / v.
Step-by-step explanation:
To determine the force exerted by a car engine moving at a constant speed, we will use the relationship between power, force, and velocity. Power (P) is the rate at which work is done or energy is transferred, and it can be expressed as the product of force (F) and velocity (v), given by P = F × v. As the car's engine produces power relative to its mass, we can calculate the total power output of the engine first.
In this scenario, the engine develops 500 watts for every kilogram of its mass. With the engine mass of 150 kg, the total power output (P) is 150 kg × 500 W/kg = 75,000 watts (or 75 kW). Since the car is moving at a velocity (v) of 20 m/s, we can rearrange the power equation to solve for force, resulting in F = P / v.
Substituting the given values into the equation yields: F = 75,000 W / 20 m/s = 3,750 newtons. Therefore, the force exerted by the engine to maintain the car's speed of 20 m/s is 3,750 newtons.