A car of mass 639.2 kg is driven along a straight flat road by an engine that provides a constant driving force. It travels at a constant speed of 11 m s-1 over a distance of 1111 meters. Assume that friction and air resistance forces remain constant at a total of 277.3 N. What is the power developed by the engine?

Question

BlackTom AI · Accepted Answer

Power equals force times velocity, so the engine power is the driving force multiplied by the car’s speed.

1) Relevant concepts
- For constant speed, acceleration is zero so the driving force exactly balances resistive forces (friction + air resistance). 
- Instantaneous mechanical power delivered by a force acting in the direction of motion is P = F · v. 
- Alternatively, average power = work done over time = (F d) / t, with t = d / v.

2) Step-by-step reasoning
- At constant speed, driving force F_drive = resistive force = 277.3 N.
- Speed v = 11 m s^-1, so instantaneous power P = F_drive × v.

3) Intermediate calculations
- Direct power: P = 277.3 N × 11 m s^-1
  = 277.3 × 11
  = 277.3 × (10 + 1)
  = 2773.0 + 277.3
  = 3050.3 W.

- (Check using work/time) Work done against resistance over distance d = F × d:
  = 277.3 N × 1111 m
  = 308080.3 J (277.3 × 1111 = 277.3×1000 + 277.3×100 + 277.3×10 + 277.3 = 277300 + 27730 + 2773 + 277.3 = 308080.3 J).
  Time to travel d at 11 m s^-1: t = 1111 / 11 = 101 s.
  Power = work / time = 308080.3 J / 101 s = 3050.297... W ≈ 3050.3 W (same result).

4) Why this answer is correct
Because at steady speed the engine only needs to supply power to overcome the constant resistive force; multiplying that resistive force by the constant velocity gives the continuous power output. Both direct P = Fv and the work/time check give 3050.3 W.

5) Why the other options are incorrect
- a (6966583 W) and c (68976 W) are far larger than the correct F·v result and imply either a wildly different force or speed; they do not match the given numbers. 
- d (308080 W) is approximately the total work in joules except off by a factor of 1 (the actual work is 308080.3 J); it confuses energy (J) with power (W) and is two orders of magnitude too large to be power here.

6) Conclusion
The calculated engine power is 3050.3 W, which matches the provided correct answer.

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