Grade 12 · Week 07 · Monday · Day 01

The Two-Cart Mystery

Learning objective: Distinguish inertia, balanced forces and changes in velocity using Newton’s first law.

45–60 minutes · Offline practice · Local student notebook

Read and reason

Why a moving cart keeps moving

A cart need not be pushed continuously to remain in motion. Newton’s first law predicts constant velocity when the vector sum of external forces is zero in an inertial reference frame. At rest is just the special case of constant velocity equal to zero. Friction and air resistance explain why a real cart slows when pushed across a floor.

Initial velocity is not a force

A free-body diagram shows external forces on a chosen object; it does not need an arrow called motion. A 4 kg cart with 6 N right and 6 N left has zero horizontal acceleration whether its initial velocity is +3 m/s, −2 m/s or 0 m/s. In each case the velocity persists under the stated idealized constant-force model.

Frames and the meaning of equilibrium

Inertial observers moving at constant velocity relative to one another may report different velocities for the same cart, but agree that a zero-net-force body has zero acceleration. The object’s mass, speed and net force are different quantities: mass is in kilograms, speed in m/s, force in newtons.

How to make the comparison fair

Use the balanced-at-rest and balanced-while-moving presets from Week 06 or the new virtual lab. Hold mass and applied forces constant while changing only initial velocity. Compare acceleration and future displacement. A good explanation states that the model omits friction changes, collisions and changing external interactions.

Five key terms

inertia
A body's resistance to acceleration; quantified by its mass.
equilibrium
Zero vector sum of external forces; acceleration is zero in an inertial frame.
inertial reference frame
A frame where zero net force implies constant velocity.
velocity
Rate of position change with direction; one-dimensional value can be signed.
net external force
Sum of all forces from outside the defined system, measured in N.

Write an original example showing how the term applies.

Worked physics example

A 4 kg cart has +6 N and −6 N horizontal forces, so ΣFx=0 N and a=0 m/s². With v₀=+3 m/s for 2 s, Δx=v₀t=+6 m. Zero net force did not erase its motion.

Write each variable, direction, algebraic substitution and SI unit in your own solution.

Student science notebook

Write and compare two cases with identical zero net force but different starting velocities. Name one real-world effect omitted by the ideal model.

Notes save locally if browser storage is available; export to preserve a portable copy.

Daily · 4 Retrieval Questions

Open-book formative practice with explanatory feedback and an 80% correction target. Scores are browser-local and not authenticated midterms or final exams.