Figure 1.7

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

1. RED ARROW represents the current velocity vector of the particle.
2. BLUE ARROW represents the velocity vector of the particle a few seconds (determined by the slider) into the future (on a predetermined path).
3. BLACK ARROW represents the acceleration vector of the particle as calculated by the difference of the two velocity vectors and divided time difference.
4. GREEN ARROW represents the true current acceleration 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 acceleration (as the ratio of velocity change over time) and true acceleration (as the time derivative) approach each other.

The velocity vector and acceleration vector form the OSCULATING PLANE.

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..