Final answer:
The output power of the car's engine, when racing at a speed of 288 km/h against a resistance force of 5 kN, is calculated to be 400,000 Watts or 400 kW.
Step-by-step explanation:
To calculate the output power of the car's engine, given the resistance and speed, we can use the formula for power, which is the product of force and velocity (Power = Force x Velocity). The resistance force is given as 5 kN, which is equivalent to 5000 N. The car races at a speed of 288 km/h, which we need to convert to meters per second (m/s) by dividing by 3.6.
Velocity in m/s = 288 km/h ÷ 3.6 = 80 m/s
Using the formula for power:
Power = Force x Velocity = 5000 N x 80 m/s = 400,000 Watts or 400 kW
Therefore, the output power of the car's engine is 400,000 Watts or 400 kW.