A car of mass 802.9 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 7.3 kJ of work while travelling at a constant speed 12 m/s over a time period of 5.7 seconds. What was the power developed by the car engine?

Question

BlackTom AI · Accepted Answer

Power is work done per unit time, so P = W / t.

1) Relevant concepts
- Power (P) is the rate at which work (W) is done: P = W / t.
- Units: 1 kJ = 1000 J, power in watts (W) where 1 W = 1 J/s.
- The car’s mass and speed are not needed to compute power from a given work and time; constant speed implies the engine’s work goes into overcoming resistive forces, but the calculation uses only total work and time.

2) Step-by-step reasoning and intermediate calculations
- Given work: 7.3 kJ = 7.3 × 1000 J = 7300 J.
- Given time: t = 5.7 s.
- Compute power: P = W / t = 7300 J / 5.7 s.
- Divide: 7300 / 5.7 = 73000 / 57 (multiplying numerator and denominator by 10).
- 57 × 1280 = 72960, remainder 40 → 73000/57 = 1280 + 40/57 ≈ 1280.7018 W.
- Rounding to the nearest whole watt gives P ≈ 1281 W.

3) Why the correct answer is correct
- The value 1281 W directly follows from the definition P = W/t after converting kJ to J and performing the division. No other data (mass, speed) changes this direct calculation.

4) Why other multiple-choice options are incorrect
- a. 52 W is far too small and does not equal 7300/5.7.
- c. 87600 (units unspecified) likely comes from an incorrect multiplication (7300 J × 12 m/s = 87600) which mixes incompatible quantities; power is W/t, not W×speed.
- d. 109 W is also not equal to 7300/5.7 and is an incorrect division or miscalculation.

5) Conclusion
- The calculated power is approximately 1281 W, which matches the provided correct answer (1281 W).

A car of mass 802.9 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 7.3 kJ of work while travelling at a constant speed 12 m/s over a time period of 5.7 seconds. What was the power developed by the car engine?数值题

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