A car of mass 839.2 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 5.6 kJ of work while travelling at a constant speed of 12.1 m/s over a distance of 6.7 meters. What was the power developed by the car engine?

Question

BlackTom AI · Accepted Answer

Power equals work done divided by the time taken, so start with W and find t.

1) Relevant concepts:
- Power P = W / t.
- Time for constant-speed motion over distance s: t = s / v.
- Alternatively, P = F · v and F = W / s, so P = (W / s) · v — both routes give the same result.
- Mass is irrelevant here because the car travels at constant speed (no change in kinetic energy).

2) Step-by-step calculation:
- Convert work to SI: 5.6 kJ = 5600 J.
- Compute time: t = s / v = 6.7 m / 12.1 m/s = 0.553719008 s (approx).
- Compute power: P = W / t = 5600 J / 0.553719008 s ≈ 10113.0 W.

3) Alternative (force × speed) check:
- Average driving force F = W / s = 5600 J / 6.7 m ≈ 835.820 N.
- Then P = F · v = 835.820 N × 12.1 m/s ≈ 10113.0 W — same result.

4) Why the correct answer is correct:
- Using either direct W/t or F·v yields ≈1.0113 × 10^4 W, which matches choice d when rounded to the given precision.

5) Why the other options are incorrect:
- a. 65 W and c. 81 W are two orders of magnitude too small compared with 1.0×10^4 W.
- b. 3101 W is also much smaller; it would correspond to a much larger time or much smaller force/speed than given. None of these align with the numerical calculation above.

Conclusion: The power developed is approximately 1.0113 × 10^4 W, so the correct choice is d. 10113 W (matches the provided answer).

A car of mass 839.2 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 5.6 kJ of work while travelling at a constant speed of 12.1 m/s over a distance of 6.7 meters. What was the power developed by the car engine?单项选择题

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