Grade 12 · Week 03 · Thursday · Day 04

Test Constant Acceleration

Which parameters change a model's position and velocity graphs?

Objective: Design a controlled simulation of initial velocity and constant acceleration, calculate signed area, and compare output to an analytic solution.

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

Read and reason

A mathematical experiment

This week's lab models x(t)=x₀+v₀t+½at² and v(t)=v₀+at in one dimension. Select duration T and experiment with positive and negative acceleration. Record initial position, initial velocity, observer-frame speed and acceleration. Predict the final signed displacement and whether a direction reversal occurs before pressing Record Trial. The simulation uses exact ideal formulas, not sensor measurements.

Change one quantity only

To study acceleration's effect, hold x₀, v₀, T and observer velocity fixed while running a matched second trial with different a. The velocity–time plot will have a new slope. A position–time plot will change curvature. With a=0 the first graph is linear and v(t) horizontal. With a positive or negative acceleration, the curve in x(t) can bend and v(t) tilts.

Check geometry against algebra

For a linearly changing velocity, compute signed area T(vstart+vend)/2; it should match Δx from the position formula. If a reversal takes place, total path length exceeds |Δx|. For instance v₀=4 m/s, a=−2 m/s², T=4 s ends at −4 m/s, has displacement 0 m and distance 8 m. The simulator should calculate these numbers while the graph shows a velocity line crossing zero.

Limits and safe alternatives

The laboratory does not model impacts, vehicle control, human motion, air drag, curved two-dimensional paths or changing acceleration. Its graph is generated rather than measured. Students can use the bundled artificial CSV records if device inputs are inaccessible. No fast-moving projectiles, ramps or hazardous equipment should be used for these investigations.

Vocabulary

initial velocity
Velocity v0 at time t=0, measured in m/s and signed according to the chosen axis. Explain with an original example.
constant acceleration
Model assumption that acceleration has the same value at all times in a specified interval. Explain with an original example.
control
A setting held unchanged when comparing trials to isolate another setting's effect. Explain with an original example.
trial
One documented repetition of a modeled or observed investigation. Explain with an original example.
residual
Difference between an observed data value and a model's predicted value at the same independent-variable value. Explain with an original example.

Worked example

With v₀=4 m/s, a=−2 m/s² and T=4 s, vfinal=−4 m/s. Displacement=4×4+0.5×(−2)×16=0 m. Signed velocity–time area agrees and distance traveled is 8 m.

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

Your science journal

Run three controlled cases: constant velocity, speeding up and reversing. Export the model, make a labeled comparison table and explain the slope/area correspondence.

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.