A 30% efficient car engine accelerates the 1700 kg car from rest to 15 m/s. How much energy is transferred to the engine by the burning gasoline?

Question

BlackTom AI · Accepted Answer

Since the engine is 30% efficient, the chemical energy supplied must be larger than the car’s kinetic energy gain; efficiency = useful energy out / energy in.

1. Relevant knowledge points and concepts
- Kinetic energy (KE) of a moving object: KE = 1/2 m v^2.
- Efficiency (η) relates useful output energy to input energy: η = E_out / E_in, so E_in = E_out / η.
- Units: use SI (kg, m/s, J).

2. Complete reasoning process step by step
- Compute the car’s kinetic energy increase (useful output energy).
- Divide that KE by the engine efficiency (0.30) to find the chemical energy supplied.

3. Calculations with intermediate steps
- Mass m = 1700 kg, speed v = 15 m/s.
- v^2 = 15^2 = 225.
- KE = (1/2) m v^2 = 0.5 × 1700 × 225.
- 1700 × 225 = 382,500.
- KE = 0.5 × 382,500 = 191,250 J = 191.25 kJ.
- Engine efficiency η = 30% = 0.30, so energy supplied E_in = KE / η.
- E_in = 191,250 J / 0.30 = 637,500 J = 637.5 kJ.
- Rounding to match answer choices gives ≈ 640 kJ.

4. Why the correct answer is correct
Because only 30% of the chemical energy becomes kinetic energy, the input must be KE divided by 0.30. This yields about 637,500 J, which corresponds to the provided choice 640 kJ (rounded to two significant figures as in the options).

5. Why other options are incorrect
- 57 kJ: equals 30% of 191 kJ (mistakenly multiplying rather than dividing), so it underestimates required input.
- 190 kJ: approximately the kinetic energy only; ignores inefficiency.
- 720 kJ: larger than the correct computed input; not produced by KE/0.30.
- 450 kJ: does not satisfy the KE/efficiency relation and is too low.

6. Conclusion
The calculated energy supplied by the gasoline is about 637.5 kJ, which matches the provided answer choice 640 kJ. Final answer: 640 kJ.

A 30% efficient car engine accelerates the 1700 kg car from rest to 15 m/s. How much energy is transferred to the engine by the burning gasoline?Single choice

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