A car of mass 644.1 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 2.6 kJ of work while travelling at a constant speed of 14 m/s over a distance of 9.8 meters. What was the power developed by the car engine?

Question

BlackTom AI · Accepted Answer

Power equals work done per unit time, so P = W / t. Here W is 2.6 kJ = 2600 J and the car travels 9.8 m at 14 m/s, so the time to travel that distance is t = distance / speed.

1) Relevant knowledge points and concepts
- Power is the rate of doing work: P = W / t (watts = joules per second).
- If a force does work W over distance d, the average driving force is F = W / d; at constant speed v, power can also be written P = F v.
- Mass is irrelevant for the power calculation here because the car moves at constant speed (no net change in kinetic energy); the engine work goes into overcoming resistive forces.

2) Step-by-step reasoning
- Convert the given work to SI units.
- Find the time taken to travel 9.8 m at 14 m/s.
- Compute power using P = W / t (or P = F v as a check).

3) Calculations (all intermediate steps)
- W = 2.6 kJ = 2.6 × 10^3 J = 2600 J.
- t = d / v = 9.8 m / 14 m·s^-1 = 0.7 s.
- P = W / t = 2600 J / 0.7 s = 3714.2857... W ≈ 3714 W.

(Alternative check) F = W / d = 2600 J / 9.8 m = 265.306122... N. Then P = F v = 265.306122 N × 14 m·s^-1 = 3714.2857... W, same result.

4) Why the correct answer is correct
Using the definition of power as work per unit time with correct unit conversion and the correct travel time yields 3714.2857 W, which when rounded sensibly is 3714 W. The mathematics and units are consistent.

5) Why the other options are incorrect
- 4 W and 57 W are orders of magnitude too small; they would correspond to extremely long times or tiny forces and do not follow from the given W, d and v.
- 1820 W is about half the correct value; it could arise from an arithmetic error (for example, using an incorrect time or halving the work), but it does not follow from the correct W/t calculation.

6) Conclusion
The calculated power is 2600 J ÷ 0.7 s = 3714.29 W, so the correct answer is 3714 W, matching the provided answer.

A car of mass 644.1 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 2.6 kJ of work while travelling at a constant speed of 14 m/s over a distance of 9.8 meters. What was the power developed by the car engine?数值题

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