How accumulations change the legs of a journey

looking every so often

In detail, here is what is going on. Every leg of the journey is one second. In that second, the velocity accumulates a leg of the journey: a distance moved in a direction. Add these legs together to calculate the displacement so far. That is, where you’ve got to, as seen from the chosen point of view.

To predict the whole journey, just add arrows, tip to tail.

Adding arrows

You can make each leg of the journey more than one second, increasing the interval. (You could make the interval very much smaller or very much larger). For longer interval legs, the chance the velocity changes during the leg is higher, so the riskier the prediction. But making the interval very short means lots of arrows to add up. Choose the interval to get an accurate enough prediction. Test the forecast to find out if it’s good enough.

The velocity and interval set the displacement for the leg(one leg of many that make up the track). Add this displacement to the starting displacement to predict where you’ll end up.

For tracks with many legs, just keep repeating this recipe.