Looking at the graph - when was the person moving fastest? Slowest?
Can you adjust the curve so the bead drops with near constant vertical velocity?
Points off a rolling wheel make traces. What makes those traces have symmetry?
What is the quickest route across a ploughed field when your speed around the edge is greater?
A space craft is ten thousand kilometres from the centre of the Earth moving away at 10 km per second. At what distance will it have half that speed?
Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.