Explore this idea with the interactivity below . Then scroll down to see the main challenge.
Things to know :
The graph is not plotting ordinary speed against time, it is plotting vertical speed or velocity against time. Experiment with the interactivity until you can predict the graph shape a particular curve will produce.
This rail is also amazingly smooth - there's no friction or any other resistance you need to consider.
At the end of a run click on the bead to put it back at the top.
Also you can drag the bead up the vertical part of the rail to give it a faster entry onto the curve.
Just experiment and you'll soon see all the things you can control.
Can you shape the rail to produce each graph?
Explain how the features of the graph connect with the bead's behaviour on the rail. Once you've really "nailed it" why not send us your solution.
Can you, as an extra challenge, get a drop rate that's absolutely constant. The vertical velocity stays at one fixed value.
Send us a screen shot to prove that you did it, plus some text drawing attention to the qualities of the rail curve that made it possible.