Relative velocity and closing speed

Closing speed is the normal component of the relative velocity between two objects — the rate at which their distance is changing. Given two objects with position and velocity vectors, the closing speed is computed by projecting the relative velocity onto the unit vector of the line connecting them (using a dot product). A negative result means the objects are approaching; positive means they are separating. The post walks through four concrete examples to build intuition, then extends the concept to a time-dependent formulation using calculus, showing that the instantaneous closing speed equals the time derivative of the scalar distance between the objects.