Sovereign science instrument · offline and local

Motion Graph Studio

Explore the meaning of position, velocity, acceleration, signed displacement and distance traveled in two constant-velocity reference frames.

Model: x(t)=x₀+v₀t+½at², v(t)=v₀+at, x′(t)=x(t)−ut, v′(t)=v(t)−u. Motion is one-dimensional with constant acceleration.

1. Predict before running

Pick one variable to change. What will happen to the position slope, velocity slope, and signed area in the velocity–time graph?

Teal = observer frame; amber = ground frame

This is a synthetic, idealized algebraic simulator, not a physical motion sensor. No launchers, motor vehicles, outdoor stunts or hazardous moving equipment are required. No personal data leave your browser.

2. Read the graphs

Ground frameObserver frame
Position x or x′ (m) versus time (s). Slope represents velocity.
Velocity v or v′ (m/s) versus time (s). Slope is acceleration; signed area is displacement.

The plotted polylines approximate the continuous ideal model. The table below contains calculated points; positions and velocities are rounded only for display. Physical measurements would carry uncertainty.

3. Calculated data points

Ideal model outputs sampled uniformly in time (not observed measurements)
Time (s)Ground x (m)Frame x′ (m)Ground v (m/s)Frame v′ (m/s)

4. Experiment notebook

Record at least three comparable trials. Change only acceleration, initial velocity, or observer speed to distinguish which graph feature changes.

Saved simulated trials (no external server)
#x₀ (m)v₀ (m/s)a (m/s²)T (s)u (m/s)Δx′ (m)Frame distance (m)

Consider: Does changing the frame alter acceleration? Can displacement be zero while distance is positive? Why does negative acceleration not always imply slowing?