A car of mass 839.2 kg is driven along a straight flat road by an engine that provides a constant driving force. It travels at a constant speed over a distance of 1518.4 meters in 20 seconds. Assume that friction and air resistance forces remain constant at a total of 236.3 N. What is the power developed by the engine?

Question

BlackTom AI · Accepted Answer

At constant speed the net force on the car is zero, so the engine’s driving force must exactly balance the constant resistive forces (friction + air resistance). Therefore the driving force Fdrive = 236.3 N.

1) Relevant knowledge points and concepts
- For constant velocity, ΣF = 0 → driving force = resistive force.
- Power delivered by a force doing work at constant velocity is P = F · v (force times speed).
- Speed = distance / time. The car’s mass is irrelevant for power at constant speed (it matters only if there is acceleration).

2) Step-by-step reasoning
- Find the car’s constant speed from the given distance and time.
- Use P = F · v with F equal to the resistive force the engine must overcome.

3) Calculations (all intermediate steps)
- Speed v = distance / time = 1518.4 m / 20 s = 75.92 m/s.
- Driving force F = 236.3 N (to balance resistances).
- Power P = F × v = 236.3 N × 75.92 m/s.
  Compute: 236.3 × 75 = 17,722.5
           236.3 × 0.92 = 217.396
           Sum = 17,722.5 + 217.396 = 17,939.896 W.
- Rounding to appropriate precision gives P ≈ 17,940 W.

4) Why this answer is correct
Because at constant speed the engine only needs to supply power to overcome the constant resistive force; multiplying that force by the constant speed yields the required mechanical power. The arithmetic above gives 17,939.9 W, which rounds to 17,940 W.

5) Why the other options are incorrect
- Options b, c, d are orders of magnitude larger and would correspond to either much larger forces or much higher speeds; they do not follow from F = 236.3 N and v = 75.92 m/s. The mass (839.2 kg) does not change the power when speed is constant.

Conclusion: The power developed by the engine is 17,940 W, matching the provided correct answer.

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