Free-fall simulator

Instead of using the equation $s = \tfrac12 gt^2$, this program lets a stone fall in tiny steps of time. In every step it falls a little and speeds up a little. You will make the steps work, compare the result with the equation, and see how small the difference is.

The idea. In a tiny time $dt$, the stone falls $v \times dt$ and its speed grows by $g \times dt$. Repeat that many times and you have the whole fall. The equation gives the same answer in one go.

Your tasks.

1. Inside the loop, make the stone fall a little and speed up a little.
2. Work out exact, the distance the equation $s = \tfrac12 gt^2$ gives after t_end seconds.
3. Work out difference, the equation's answer minus the stepping answer.