Kinematics - Motion Graphs

Interactive kinematics tool where students draw one motion graph (position, velocity, or acceleration) and the other two are automatically calculated and displayed. Draw on a 10-second timeline using four tools: freehand (lightly smoothed), line, quadratic Bézier, or cubic Bézier. The tool numerically derives/integrates graphs in real-time: draw x(t) to get v(t) = dx/dt and a(t) = dv/dt; draw v(t) to derive acceleration; draw a(t) to integrate for velocity and position. A vertical track displays a turtle animation acting out the motion, with optional velocity/acceleration vector arrows and a motion diagram (strobe marks). Control conditions: set initial position (x₀) and initial velocity (v₀) when not drawing on the position graph. Four presets: constant velocity, speeding up, slowing down then stopped, out-and-back with turnaround. Sticky readout bar shows current t, x, v, a values; scrub bar for manual time control; play/pause/rewind and variable-speed playback (0.25×–2×). Light and dark mode. Teaches relationships between kinematic graphs via visual feedback and animation.