How to play Graph Rider
- Choose a target. The dashed line shows the velocity the cart should have at every moment.
- For each leg, read how much the velocity changes and how long the leg lasts.
- Set each leg's acceleration to its slope, Δv ÷ Δt. A flat leg needs a = 0; a falling leg needs a negative a.
- Press Play. Your trace is drawn over the target while your cart drives beside the target cart. Pause or step to read the meters.
Acceleration is the slope of a velocity–time graph
Acceleration is the rate at which velocity changes: a = Δv ÷ Δt. On a v–t graph, that is the slope. A rising line means positive acceleration, a falling line negative acceleration, and a flat line zero acceleration, even if the object is moving fast. The area between the graph and the time axis is the displacement; area below the axis counts as negative.
A focused learning model
The track is straight and the cart is treated as a point. On each leg the acceleration is exactly constant, and it changes instantly between legs, so the v–t graph is made of straight pieces while the velocity itself never jumps. Position and velocity come from exact formulas, and the run plays in real time.