Grade 12 · Week 02 · Thursday · Day 04

Build a Motion Graph Laboratory

Can a single object have different displacements in moving frames?

Objective: Investigate how initial position, initial velocity and a chosen moving reference frame change position graphs and measured displacement.

45–60 minutes · Offline-capable · Public practice is not a supervised examination

Read and reason

Use a model with known assumptions

Our offline studio describes one-dimensional motion mathematically. Choose starting position x₀, starting velocity v₀, acceleration a, elapsed time T and an observer-frame speed u. The position function is x(t)=x₀+v₀t+½at². To isolate the Week 02 velocity idea, first set acceleration to zero. The function is a model of prescribed motion, not a sensor connected to a real person or vehicle.

Change one variable at a time

Predict what will happen if you change observer speed from u=0 to u=+2 m/s while holding x₀, v₀, a and T constant. In the moving frame, x′(t)=x(t)−ut; the measured velocity shifts by −u. The two frames describe the same modeled object. Compare the plotted endpoints and slopes, and explain why the difference belongs to a changed reference frame.

Compare distance with displacement

For Week 02, choose two or more simple nonaccelerating cases, then try one reversing case by changing acceleration. A model with a constant nonzero acceleration can reverse direction if v(t) crosses zero within the interval. The signed displacement remains x(T)−x₀; traveled distance adds the absolute lengths of each segment. The studio explicitly calculates distance for up to one turning point under constant acceleration.

Do not confuse simulation with evidence from a sensor

The plotted values are exact outputs of ideal equations to the displayed precision. Physical motion measurements would include sampling error, air resistance, friction, instrument precision and other unmodeled effects. State which assumptions underlie your result. If you want a safe real alternative, use a small soft toy in an open indoor area with no ramps, no collisions and no recording of other people, or analyze the supplied dataset instead.

Vocabulary

prediction
A testable statement about a model result before the trial is run. Explain with an original example.
variable
A quantity or condition that can change; use a controlled comparison to isolate effects. Explain with an original example.
trial
One documented repetition of a modeled or observed investigation. Explain with an original example.
dataset
A named collection of values with variables, units, and provenance. Explain with an original example.
uncertainty
The limits of confidence or precision in measurements and inference. Explain with an original example.

Worked example

Model x₀=0 m, v₀=3 m/s, a=0, T=4 s. Ground displacement is +12 m; frame u=+1 m/s gives displacement +8 m. The initial positions coincide at t=0.

Check signs and units. Show each calculation rather than memorizing a number.

Your science journal

Record a prediction and three runs, comparing matched parameters except the observer-frame speed. Export your results and calculate each graph's slope.

Journal lives in this browser if localStorage is permitted; export backups to keep it.

Daily Retrieval Practice · 4 Questions

Choose one answer to each question, check, read the feedback, and retry after correcting mistakes. Target 80% open-book mastery; public practice scores do not authenticate official midterms or finals.