A car of mass 615.2 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 2.3 kJ of work while travelling at a constant speed 13.2 m/s over a time period of 3.3 seconds. What was the power developed by the car engine?

Question

BlackTom AI · Accepted Answer

Power = work / time, so compute P = (2.3 kJ) / (3.3 s).

1) Relevant knowledge points and concepts
- Power is the rate at which work is done: P = W / t.
- Work given in joules; convert kilojoules to joules (1 kJ = 1000 J).
- When a vehicle moves at constant speed, net change in kinetic energy is zero; the engine’s work goes into overcoming resistive forces. The car’s mass and speed are not needed to compute average power from the work done and time, but they can be used to check consistency via P = F v (force × speed).

2) Step-by-step reasoning and intermediate calculations
- Convert work to joules: W = 2.3 kJ = 2.3 × 1000 J = 2300 J.
- Time: t = 3.3 s.
- Compute power: P = W / t = 2300 J / 3.3 s.

3) Calculation with intermediate steps
- 2300 ÷ 3.3 = 2300 ÷ 3.3
- 3.3 × 700 = 2310, so the exact quotient is slightly less than 700.
- Doing the division: 2300 / 3.3 ≈ 696.969696... W.
- Round to three significant figures: P ≈ 697 W.

(As a consistency check: distance traveled s = v t = 13.2 m/s × 3.3 s = 43.56 m. Average resistive force F = W/s = 2300 J / 43.56 m ≈ 52.79 N. Then P = F v ≈ 52.79 N × 13.2 m/s ≈ 696.9 W — same result.)

4) Why the correct answer is correct
Because power is defined as work per unit time and we used the given total work and time, the computed value 2300 J / 3.3 s = ~697 W is the correct power developed by the engine during that interval.

5) Why the other options are incorrect
- a) 49 W is far too small compared to 2300 J over 3.3 s.
- b) 30360 W is about 44 times larger than the correct value and might come from a misconceived use of mass or kinetic-energy formulas.
- c) 12 W is also far too small.
- d) 697 W matches the correct calculation.

Conclusion: The power developed by the car engine is 697 W, matching the provided answer.

A car of mass 615.2 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 2.3 kJ of work while travelling at a constant speed 13.2 m/s over a time period of 3.3 seconds. What was the power developed by the car engine?数值题

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Work and power help us understand how force is applied across distance and how quickly that work is done over time (T or F)

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