A car of mass 1364 kg is subject to a net force of 3168 N forward. What is the car's acceleration? (Give your answer to one decimal point.)

Question

BlackTom AI · Accepted Answer

Newton's second law, F = ma, gives the direct relation between net force, mass, and acceleration.

1) Relevant knowledge points and concepts
- Newton's second law: net force F (in newtons) equals mass m (in kilograms) times acceleration a (in m/s^2).
- Units must be consistent: N = kg·m/s^2, so solving a = F/m yields acceleration in m/s^2.
- Rounding: to one decimal place, examine the hundredths digit to decide rounding of the tenths digit.

2) Complete reasoning process step by step
- Given: F = 3168 N, m = 1364 kg.
- Apply a = F/m.

3) Calculations with intermediate steps
- a = 3168 N / 1364 kg.
- Simplify the fraction by dividing numerator and denominator by 4: 3168 ÷ 4 = 792, 1364 ÷ 4 = 341, so a = 792/341.
- Perform the division: 792 ÷ 341 = 2 remainder 110 (since 341 × 2 = 682; 792 − 682 = 110).
- Convert remainder to decimal: 110/341 ≈ 0.32258..., so a ≈ 2.32258... m/s^2.
- Round to one decimal place: the tenths digit is 3 and the hundredths digit is 2 (<5), so round down to 2.3 m/s^2.

4) Why the correct answer is correct
- The calculation directly follows F = ma with correct units and arithmetic; the decimal approximation 2.32258... rounds to 2.3 when reporting to one decimal place.

5) Why other answers would be incorrect
- Using m/F instead of F/m would produce ≈0.43 (wrong orientation).
- Forgetting units or using grams instead of kilograms would change the magnitude by a factor of 1000.
- Rounding improperly (e.g., to 2.4) would be incorrect because the hundredths digit is 2, not ≥5.

6) Conclusion and confirmation
- The car’s acceleration is 2.3 m/s^2, which matches the provided answer (2.3).

A car of mass 1364 kg is subject to a net force of 3168 N forward. What is the car's acceleration? (Give your answer to one decimal point.)Numerical

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