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 the rate at which work is done, so P = W / t.

Relevant points:
- Convert energy to SI: 5.6 kJ = 5600 J.
- Time to travel the distance at constant speed: t = distance / speed.
- At constant speed the engine’s work goes into overcoming resistive forces (not changing kinetic energy), so mass is irrelevant for the numerical power calculation here.

Step-by-step calculation:
1. Convert work: W = 5.6 kJ = 5.6 × 10^3 J = 5600 J.
2. Compute time: t = d / v = 6.7 m / 12.1 m·s^-1.
   - t = 6.7 / 12.1 = 0.553719... s (≈ 0.55372 s).
3. Compute power: P = W / t = 5600 J / 0.553719 s.
   - P ≈ 5600 / 0.553719 = 10113.0 W.

Alternative check using force and velocity:
- Driving force F = W / d = 5600 J / 6.7 m ≈ 835.8209 N.
- Then P = F v = 835.8209 N × 12.1 m·s^-1 ≈ 10113.0 W, same result.

Why the other options are incorrect:
- 81 W and 65 W are orders of magnitude too small given 5600 J delivered in about half a second; they would correspond to times of many tens of seconds, not 0.55 s.
- 3101 W is also too small; it would correspond to a longer effective time (~1.8 s) or a smaller work input than given.

Conclusion: The computed power is approximately 1.0113 × 10^4 W, i.e. 10113 W, which matches the provided correct 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?数值题

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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?

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