# Cycling Motion Equations

### Dynamic  Motion Equations

Not every riding scenario involves riding at a constant speed. You have start ups, speed changes, descents, and slow downs. Here we are interested in what happens dynamically with the cycle rather than the cyclist, and are looking for the Scenario Motion Equations.

These are the v(t) and x(t) equations we discussed earlier when we focused on the solutions to the Cycling Force Equation. These can be solved directly but with some mathematical challenges, or using incremental techniques which yield the graphs but not the underlying formulas.

Classical Mechanics describes how objects move when subjected to external forces. An object’s motion is quantified by deriving its equations of motion from its force equation. This process is perfectly applicable to analyzing cycling dynamics and is what we outlined in our section on the Cycling Force equation

### How valuable are these equations?

If you are looking to understand how the bike behaves when subjected to forces, these equations are critical. But once you understand that, the use of these in your daily riding drops off dramatically, particularly when compared to Power Models.

Next Topic:   Energy Models