The rate machine — a velocity does something every secondhops, not formulas
A steady velocity is a promise: every second, the position changes by this many metres — sign and all. Set the promise, then press +1 second and watch it kept: one hop on the track, one new event in the table, one more piece of the line.
velocity v = m/s start position x₀ = m
clock starts at t = s
Event table (one row per second)
Commit first — ink, then the machine.
The clock reads 2 s and the walker is at x = 1 m, moving at a steady +2.5 m/s. Where is the walker when the clock reads 6 s?
clock reading t = —position x = —this second: —
Teacher: before each press, point at a student: where will it be after this second? Then press. Re-set with v = −1.5 from x₀ = 7 and repeat — the promise is kept leftward. No formula appears anywhere in this scene.
Two walkers, one meetingthe freeze-frame question
Walker A and Walker B walk along the same straight track. The graph plots both positions against the clock reading. Play the motion; it pauses itself at the moment they meet. Commit both answers in ink before Reveal.
Closing in on an instantthe shrinking interval, from both sides
The walker’s motion follows the curve shown. The marked instant is t = 4 s. Each button computes an average velocity over an interval that ends — or begins — at that instant, and draws its chord. Commit before you press the two finest buttons.
Chords from the left (interval ends at 4 s)
Chords from the right (interval begins at 4 s)
Commit — ink first.
Every interval on those buttons has t = 4 s as one of its two ends. Will making such an interval small enough ever give an average velocity exactly equal to the velocity at t = 4 s?
Out and back — two averages, one journeythree freezes · commit at each
One walker: out fast, back slower. The motion pauses itself three times. At each pause, commit in ink, then press Continue. Reveal comes only at the end.
Builder — velocity editionsegments of steady velocity · pin a claim · resolve conflicts
Build a motion out of segments of steady velocity — each segment says: for this many seconds, the walker’s position changes by this many metres each second. Then pin a claim of your own (“at t = …, x = …”) and see whether your claims agree. The four cards are the judges.
Your model
Start position x₀ = m
Pin a claim
at t = s , x = m
Challenges