Motion-Change: x = x + v*dt or dx = v*dt

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).

Watch and play with this code.

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 \frac{dx}{dt} = v), 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.