From the archive, Tuesday 1 September 2026
Kinematics, 2 of 2, Slopes, Areas, and Reference Frames
A motion graph answers two different questions, and they are not the same question. The slope tells you a rate. The area tells you an accumulation. Read the wrong one and every number after it is wrong in a way that looks tidy. Then a second idea, which is that every graph on this page was drawn by somebody, and somebody else moving past would have drawn a different one. Three questions, each harder than the last. You unlock the next by answering the one you are on.
Level 1: PhD dropout
On a velocity against time graph, a cart’s velocity falls along a straight line from +15 m/s at t = 0 to -5 m/s at t = 5.0 s. Find the cart’s acceleration, in m/s2.
About 2 minutes. Watch out for stopping at the change in velocity, which is not yet a rate.
Levels 2 and 3
Level 2, CalTech, opens once you have cleared Level 1, and it comes with every hint. Level 3, Lucasian, needs a class code. Nothing on an archived day is recorded, and nothing counts toward a leaderboard.
The interactive version of this day, with the tutor and the calculus companions, loads here when your browser runs the page script. See also today’s question and the rest of the archive.