A 4.1 tonne truck does 44.7 kJ of work while travelling up a slope at constant speed. It takes 17.2 seconds to travel a distance of 179.1 m. The power exerted by the truck engine is:

Question

BlackTom AI · Accepted Answer

Power is the rate at which work (energy) is done: P = W / t.

Relevant knowledge and concepts:
- Work (W) must be in joules (J) and time (t) in seconds (s) to get power in watts (W).
- 1 kJ = 1000 J.
- When the problem gives the work done and the time taken, the power is simply work divided by time; other data (mass, distance) are unnecessary for the numerical power calculation once work and time are known.

Step-by-step reasoning and calculations:
1. Convert the given work from kilojoules to joules:
   W = 44.7 kJ = 44.7 × 1000 J = 44,700 J.
2. Use the given time (17.2 s) directly.
3. Compute power:
   P = W / t = 44,700 J / 17.2 s.
4. Perform the division:
   44,700 ÷ 17.2 = 2,598.8372093... W.
5. Round to two decimal places (matching the answer choices): P ≈ 2,598.84 W.

Why this answer is correct:
- The definition P = W/t directly applies and yields 2,598.84 W when using the properly converted units. The truck’s mass and the distance traveled are not needed because the total work already accounts for all forces and energy changes; power depends only on how quickly that work is done (time).

Why the other choices are incorrect:
- a (4654.52 W), b (3844.20 W), and d (3405.74 W) do not equal 44,700 J ÷ 17.2 s and therefore do not match the correct application of P = W/t with the given numbers.

Conclusion:
The calculated power is 2,598.84 W, which matches the provided correct answer (option c).

A 4.1 tonne truck does 44.7 kJ of work while travelling up a slope at constant speed. It takes 17.2 seconds to travel a distance of 179.1 m. The power exerted by the truck engine is:单项选择题

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