Net force, mass & acceleration
You will be able to: Use a signed force sum to predict acceleration and interpret force–acceleration data.
What changes when you push harder or load the cart?
An empty shopping cart responds strongly to a push. The same push changes a loaded cart’s velocity more slowly. What matters is both the net push and the total mass being accelerated.
A useful starting point: Free-body diagrams →
Words and symbols before equations
- Net force ΣF
- Vector sum of all external forces, in N.
- Mass m
- Inertia in kg; must be positive.
- Proportional
- Doubling one quantity doubles another when the other relevant factors stay fixed.
What this picture assumes
Horizontal net-force investigation: right is positive. Resistance is a prescribed force, not a static-friction solver. Vertical support balances weight; g=10 m/s². Velocity is not specified.
Connect the picture to the physics
Newton’s second law is ΣF=ma for a fixed-mass system in an inertial frame. Add forces with signs first; only then divide by mass. Apply the law separately along perpendicular axes.
The acceleration points with net force, not necessarily with velocity. A rightward force can slow an object that is moving left before it reverses.
At fixed mass, plotting net force vertically against acceleration horizontally gives slope m. Slope means rise divided by run: N/(m/s²)=kg. A force-versus-time graph alone does not give acceleration until mass is known.
A worked example, step by step
A 4 kg cart is pulled 14 N right while 6 N resistance acts left. Find acceleration and velocity after 3 s if it starts from rest and the forces stay constant.
- Choose right positive and draw the two horizontal forces.
- Net force = 14−6 = 8 N right.
- a = 8/4 = +2 m/s².
- Velocity change in 3 s is aΔt = 6 m/s, so final velocity is +6 m/s. Each second adds 2 m/s.
Do not substitute one applied force for net force when other forces also act.
A force points right while velocity points left. Must the object already be moving right?
Compare with an explanation
No. It accelerates right; initially it slows its leftward motion.
Predict. Change one thing. Explain.
Hold resistance at 0 N. Compare 4 N and 8 N applied to a 2 kg cart. Then keep net force 8 N and double the mass. Explain both proportional changes.
Net horizontal force 5 N; acceleration 2.5 m/s² (right positive). Force arrows share a scale of 4.75 drawing units/N.
Horizontal net-force investigation: right is positive. Resistance is a prescribed force, not a static-friction solver. Vertical support balances weight; g=10 m/s². Velocity is not specified.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a force or motion relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionFor a fixed cart, measured (a,F_net) pairs are (1 m/s²,3 N), (2 m/s²,6 N), and (3 m/s²,9 N). (a) Describe the graph, (b) infer mass, (c) predict force for 4 m/s², and (d) name one experimental control.
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Compare with the answer and four-point rubric
- 1 point: A straight line through the origin.
- 1 point: Slope 3 N/(m/s²) = 3 kg.
- 1 point: 12 N.
- 1 point: Keep the same cart mass; account for resistance when determining net force. Repeat measurements to assess variation.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Which force goes into F=ma?
The vector sum of external forces.
RECALL 2Double mass at fixed net force?
Acceleration halves.
RECALL 3What does a force–acceleration slope measure?
Mass, when force is on the vertical axis.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Net force, mass & acceleration
- ΣF_x = ma_x and ΣF_y = ma_y.
- a = F_net/m; fixed-mass, inertial-frame model.
Remember: Do not substitute one applied force for net force when other forces also act.
Conditions: Horizontal net-force investigation: right is positive. Resistance is a prescribed force, not a static-friction solver. Vertical support balances weight; g=10 m/s². Velocity is not specified.
Refresh Kid · Unit 2 · Objectives 2.5.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.5, objectives 2.5.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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