A 5.7 tonne truck does 34.5 kJ of work while travelling up a slope at constant speed. It takes 11.8 seconds to travel a distance of 127.1 m. The power exerted by the truck engine is:

Question

BlackTom AI · Accepted Answer

Power equals work done divided by the time taken, so P = W / t.

Relevant concepts:
- Work (energy) must be in joules (J). 1 kJ = 1000 J.
- Power is the rate of doing work, measured in watts (W), where 1 W = 1 J/s.
- Average power over an interval = total work / total time.

Step-by-step calculation:
1. Convert the given work from kilojoules to joules:
   W = 34.5 kJ = 34.5 × 1000 J = 34,500 J.
2. Use the time given directly:
   t = 11.8 s.
3. Compute average power:
   P = W / t = 34,500 J / 11.8 s.
   Perform the division: 34,500 ÷ 11.8 = 2,923.72881356... W.
4. Round to two decimal places (as in the choices): P ≈ 2,923.73 W.

Why this is correct:
- The engine’s power output is defined by how much work it does per second. The problem explicitly gives total work and the time interval, so the direct ratio gives the average power. The truck’s mass and the distance traveled are not needed for this calculation because the numerical work (34.5 kJ) and the time (11.8 s) are already provided; the constant speed condition simply implies no change in kinetic energy, so the supplied work is expended against gravity and friction and is the figure to use.

Why the other options are incorrect:
- Options a, b, and d do not equal 34,500 J divided by 11.8 s, so they do not represent the correct power given the provided work and time. Only option c matches the correct arithmetic result.

Conclusion:
The calculated power is 2,923.73 W, confirming the correct answer is c. 2923.73 W.

A 5.7 tonne truck does 34.5 kJ of work while travelling up a slope at constant speed. It takes 11.8 seconds to travel a distance of 127.1 m. The power exerted by the truck engine is:单项选择题

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