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Net Force and Acceleration

A public mechanics question that shows how to combine opposing horizontal forces before applying Newton's second law.

Question

A 4.0 kg4.0\,\text{kg} cart is pulled horizontally with 18 N18\,\text{N} to the right while friction exerts 6 N6\,\text{N} to the left. What is the cart's horizontal acceleration?

  1. a.1.5 m/s21.5\,\text{m/s}^2 to the right
  2. b.3.0 m/s23.0\,\text{m/s}^2 to the right
  3. c.4.5 m/s24.5\,\text{m/s}^2 to the right
  4. d.6.0 m/s26.0\,\text{m/s}^2 to the right

Correct answer

B. 3.0 m/s23.0\,\text{m/s}^2 to the right

Full reasoning

  1. 1Choose the cart as the system and take right as positive.
  2. 2Add the horizontal forces with signs: ∑Fx=18 N−6 N=12 N\sum F_x = 18\,\text{N} - 6\,\text{N} = 12\,\text{N}.
  3. 3Apply ax=∑Fx/m=12 N/4.0 kga_x = \sum F_x/m = 12\,\text{N}/4.0\,\text{kg}.
  4. 4The acceleration is 3.0 m/s23.0\,\text{m/s}^2 to the right, so choice B is correct.

Why each choice is right or wrong

Choice A

This divides the friction force alone by the mass and ignores the applied force.

Choice B

Correct. The net force is 18−6=12 N18 - 6 = 12\,\text{N}, and 12/4.0=3.0 m/s212/4.0 = 3.0\,\text{m/s}^2.

Choice C

This divides the applied force by the mass without subtracting friction.

Choice D

This adds the opposing force magnitudes instead of taking their signed vector sum.

Related formula

Newton's second law for constant mass

∑F⃗ext=ma⃗\sum \vec{F}_{\text{ext}} = m\vec{a}

Assumptions: Mass is constant. The component equation uses one declared positive direction.

Related topic and practice

Newton's Second Law and Free-Body DiagramsClassical Mechanics Domain GuideEnergy and Momentum ConservationSimple Harmonic MotionA collision that conserves momentum but loses kinetic energyEnergy Conservation on a Frictionless TrackCreate a free account to practice

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 1, Section 5.3: Newton's Second Law — OpenStax. Accessed 2026-07-06. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-07-17

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