Draw the graphs from the data

A cyclist's position is written down every $2$ seconds. You will make the program find her velocity in each gap, add up the area under the velocity graph to get the distance, and find when she was fastest. Then it draws both graphs.

The idea. In each gap, velocity $=$ change of position $\div$ change of time (the slope). Each gap is a strip $2\ \text{s}$ wide under the velocity graph, so its area is velocity $\times 2$. The areas add up to the distance.

Your tasks.

1. Work out the velocity in each gap and add it to the list velocities.
2. Add up the area under the velocity graph, area.
3. Find fastest, the time at the start of the gap where she was fastest.