Figure 1.6

To compute the velocity vector using the inertial frame, take the difference in two position vectors and divide that by the time difference. In the figure below:

1. RED ARROW represents the current position vector of the particle.
2. BLUE ARROW represents the position vector of the particle a few seconds (determined by the slider) into the future (on a predetermined path).
3. BLACK ARROW represents the velocity vector of the particle as calculated by the difference of the two position vectors and divided time difference.
4. GREEN ARROW represents the true current velocity vector of the red particle.

THE ACT OF MOVING THE SLIDER TO THE LEFT IS EQUIVALENT TO TAKING THE LIMIT AS DT GOES TO ZERO. As the interval approaches zero, the calculated velocity (as the ratio of position change over time) and true velocity (as the time derivative) approach each other.

As an aside, the presented curve is Viviani's Curve. It represents the intersection of a sphere with a cylinder. To create the curve, one edge of the cylinder is tangent to the sphere and another edge passees through the center of the sphere..