The Lamborghini Huracan, when driven with no passengers (other than the driver), has an initial acceleration of 0.65g. Its mass, with a driver, is 1510 kg. If a 90 kg passenger rode along, what would the car's acceleration be (assuming the car provided the same force)?

Question

BlackTom AI · Accepted Answer

Acceleration scales as a = F/m, so if the car produces the same driving force and you increase the mass, the acceleration decreases in inverse proportion to the mass.

1) Relevant knowledge points and concepts
- Newton’s second law: F = m a, so a = F/m.
- If the propulsion force F is unchanged, acceleration is inversely proportional to the total mass.
- “0.65 g” means 0.65 times the acceleration due to gravity (g ≈ 9.8 m/s^2).

2) Complete reasoning process step by step
- Determine the force the car produces when accelerating the 1510 kg vehicle at 0.65 g.
- Use that same force and divide by the new total mass (1510 kg + 90 kg = 1600 kg) to find the new acceleration.
- Express the result in units of g to compare with the original 0.65 g.

3) Intermediate calculations
- Convert 0.65 g to m/s^2: 0.65 × 9.8 m/s^2 = 6.37 m/s^2.
- Compute the driving force: F = m a = 1510 kg × 6.37 m/s^2 = 9618.7 N.
- New mass: m' = 1510 + 90 = 1600 kg.
- New acceleration: a' = F / m' = 9618.7 N / 1600 kg = 6.0116875 m/s^2.
- In units of g: a' / g = 6.0116875 / 9.8 ≈ 0.61344 g ≈ 0.61 g.

4) Why the correct answer is correct
Because F is assumed constant, the new acceleration follows directly from a' = (1510/1600) × 0.65 g = 0.6134 g. This reduction is the expected inverse-mass scaling from Newton’s second law.

5) Why other answers would be incorrect
Common mistakes would include failing to add the passenger mass (using 1510 kg instead of 1600 kg), converting g incorrectly, or using subtraction rather than the inverse proportional scaling. Any result significantly different from ~0.61 g stems from these errors.

6) Conclusion confirming final answer
The car’s acceleration with the 90 kg passenger aboard is approximately 0.61 g, which matches the provided correct answer.

The Lamborghini Huracan, when driven with no passengers (other than the driver), has an initial acceleration of 0.65g. Its mass, with a driver, is 1510 kg. If a 90 kg passenger rode along, what would the car's acceleration be (assuming the car provided the same force)?单项选择题

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