Separate equilibrium from being at rest

1. Orient: Separate equilibrium from being at rest

Newton’s first law describes inertial motion: with zero net external force, velocity remains constant. Rest is one possible constant velocity, not the only one. A cart gliding at 3 m/s on an ideal frictionless horizontal track requires no forward force to maintain that velocity.

2. Explain and derive

Equilibrium in translation means the force components sum to zero, so acceleration is zero. It does not require every individual force to vanish. Equal leftward and rightward pushes can coexist with motion. Conversely, a momentary zero velocity does not imply balanced forces: an object turning around can have nonzero acceleration.

Choose a positive direction before adding forces. With rightward force R and leftward magnitude L on a 2 kg object, a=(R−L)/2. If initial velocity is positive but R<L, the object initially slows. Continued negative acceleration can later reverse the motion and increase speed in the negative direction.

An inertial frame is necessary for the simple statement Fnet=ma without additional apparent-force terms. A speeding-up vehicle is not an inertial observer for this purpose. Do not interpret a passenger’s apparent backward motion as evidence of an extra backward interaction unless an actual agent supplies it.

3. Work an example

With 8 N left and 8 N right, the net horizontal force is 0 and the initial+3 m/s velocity remains+3 m/s after 2 s. With 12 N left and 8 N right, a=−2 m/s² and final velocity is 3−2×2=−1 m/s. The object has reversed even though the force directions never changed.

4. Predict and investigate

Predict first: Can both forces be nonzero while acceleration is zero? Can velocity be zero while acceleration is nonzero?

Begin with equal forces and verify constant nonzero velocity. Increase only the leftward force, then only the rightward force. Predict whether the object initially speeds up or slows down and whether it reverses within 2 s. Explain the motion using signs rather than “positive force means forward motion.” Use the lesson controls and record the settings with your evidence.

5. Transfer and explain

Try a new practice case

A 2 kg cart starts at+3 m/s. A constant net force of−4 N acts for 1 s. Find final velocity.

Your numerical result (m/s) Check number

Reveal worked check (practice, not mastery)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Reflect and retain evidence

How would repeated velocity measurements distinguish equilibrium from a turning point observed in a single image?

Retain your first answer, force diagram, equations, units, assumptions and a changed-case prediction. Public worked checks are practice, not independent mastery evidence. Supplied synthetic outputs do not certify actual laboratory skill.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 2 topic mapping: 2.4; 2.5. Checked 30 October 2026. This is a content cross-reference, not AP authorization.