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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Question

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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BlackTom AI · Accepted Answer

Power is the rate of doing work, so P = W / t (watts = joules per second). Because the car travels a known distance at constant speed, we can find the time taken and thus the power.

1) Relevant concepts
- Work W is energy transferred (given as 2.6 kJ = 2600 J).
- Power P = W / t.
- For motion at constant speed, time t = distance / speed.
- Alternatively, P = F v where F = W / distance is the driving force and v is speed; both approaches agree.

2) Step-by-step reasoning and intermediate calculations
- Convert work to SI units: W = 2.6 kJ = 2600 J.
- Compute time to travel 9.8 m at 14 m/s:
  t = d / v = 9.8 m / 14 m/s = 0.7 s.
- Compute power from P = W / t:
  P = 2600 J / 0.7 s = 3714.2857... W.

(Alternative check using force and P = F v)
- Driving force F = W / distance = 2600 J / 9.8 m = 265.306122... N.
- Then P = F v = 265.306122 N * 14 m/s = 3714.2857... W.

3) Why this answer is correct
- The engine does 2600 J of work in 0.7 s, so the average power output during that interval is 2600/0.7 W ≈ 3714 W. Both the direct W/t method and the F·v method give the same value, confirming consistency.

4) Why the other options are incorrect
- 57 W and 4 W are orders of magnitude too small compared with 2600 J performed in less than a second.
- 1820 W is also too small (roughly half the correct value) and does not match the required W/t calculation.

Conclusion: The power developed by the car engine is approximately 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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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?

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