Motion is change of position x with a certain rate of change as velocity v according to the code
- x = x + v*dt;
where dt is a time step. Notice that the the code expresses
- x_new = x_old + v*dt that is x_new – x_old = v*dt or
- dx = v*dt with dx = x_new – x_old (compare with Newton Header).
This code expresses mor generally any type of change of a quantity x with a certain rate of change v over a time step dt.
The code is interpreted as
- x_new = x_old + v*dt
where x_old is a given value which with rate v changes over a time step dt into a new value x_new, which can be expressed as
- dx = v* dt with dx = x_new – x_old,
where dx = x_new – x_old is the change of x over the time step as change of time. The code x = x + v*dt thus has the meaning
- dx = v*dt
which we, in the form dx/dt = v (or ), will discover as the essence of the wonderful Calculus created by Newton and Leibniz in 17th century as the
- mathematics and science of change
which will be the basic tool to construct-simulate-understand the world.