Inertia and constant velocity
You will be able to: Distinguish zero acceleration from zero velocity in an inertial frame.
Does something moving right need a net force right?
Imagine a puck already sliding right on nearly frictionless ice. Once the push stops, it keeps moving. A continuing push is needed to overcome resistance in everyday life, not to sustain motion itself.
A useful starting point: Acceleration and signs →
Words and symbols before equations
- Inertia
- Resistance to changes in velocity; greater mass means greater inertia.
- Equilibrium
- Zero net force; here, translational equilibrium.
- Inertial frame
- A nonaccelerating reference frame where Newton’s first law holds.
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
When external forces sum to zero, velocity stays constant. Constant velocity includes rest but also straight-line motion at a steady speed.
A puck sliding at 3 m/s right can have zero horizontal force. If a 2 N pull right balances 2 N resistance left, it also has zero horizontal net force. Different force lists can produce the same acceleration.
In a bus that brakes, an unrestrained object seems to move forward relative to the bus. From the road’s approximately inertial frame it tends to keep its previous velocity. Do not invent a real forward interaction merely to explain the bus-frame appearance.
A worked example, step by step
A box moves right at 2 m/s. A rope pulls 6 N right while friction acts 6 N left. Its mass is 3 kg. Describe the next 4 s if these forces stay constant.
- Take right positive: horizontal net force is 6−6 = 0 N.
- Zero net force gives zero acceleration. The box keeps velocity +2 m/s.
- In 4 s its displacement is 2×4 = +8 m.
- Zero net force did not stop the box; it prevented any velocity change.
Zero net force does not mean no individual forces, and it does not mean zero velocity.
Can a car turning at constant speed have zero net force?
Compare with an explanation
No. Its velocity direction changes, so it accelerates.
Predict. Change one thing. Explain.
Set applied force equal to resistance. Keep mass fixed. Read the zero acceleration and explain both a stationary and a moving situation consistent with that result.
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 questionA cart travels left at 4 m/s while two horizontal forces of 5 N oppose each other. (a) Find net force, (b) give acceleration, (c) find displacement in 3 s with right positive, and (d) describe the velocity-time graph.
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Compare with the answer and four-point rubric
- 1 point: 0 N.
- 1 point: 0 m/s².
- 1 point: −12 m.
- 1 point: A horizontal line at −4 m/s; its zero slope represents zero acceleration.
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 1Does equilibrium require rest?
No; constant straight-line velocity is also possible.
RECALL 2What does inertia resist?
Changes in velocity, not motion itself.
RECALL 3Why distinguish reference frames?
A frame accelerating relative to an inertial frame changes how motion appears.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Inertia and constant velocity
- ΣF = 0 → a = 0 → constant velocity in an inertial frame.
- For constant velocity, Δx = vΔt.
Remember: Zero net force does not mean no individual forces, and it does not mean zero velocity.
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 2.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.4, objectives 2.4.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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