(1)

where is the radius vector and is the derivative with respect to time. Expressed in terms of the arc length,
(2)

where is the unit tangent vector, so the speed (which is the magnitude of the velocity) is
(3)

(1)

where is the radius vector and is the derivative with respect to time. Expressed in terms of the arc length,
(2)

where is the unit tangent vector, so the speed (which is the magnitude of the velocity) is
(3)

Weisstein, Eric W. "Velocity." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/Velocity.html