# Instantaneous speed and inverse

This post relates to the previous one here.

Speed is the time rate of distance traversed. Pace is the space rate of elapsed time.

The (time) speed of a body is the distance traversed per unit of independent time without regard to direction, Δx/t. The instantaneous speed is the speed at a point in space and time: dx(t)/dt. It is the reciprocal of the instantaneous pace, 1/(dt/dx(t)).

The inverse speed (time pace) of a body is reciprocal of the speed, 1/(Δx/t) ≈ Δtx. The instantaneous pace is the pace at a point in space and time: 1/(dx(t)/dt) ≈ dt/dx(t). It is the reciprocal of the puncstanceous speed dx(t)/dt.

The (space) pace of a body is the traversal time per unit of independent distance without regard to direction, Δt(x)/x. The puncstanceous pace is the pace at a point in time and space: dt(x)/dx.

The inverse pace (space speed) of a body is the reciprocal of the pace, 1/(Δt(x)/x) ≈ Δx/Δt(x). The puncstanceous speed is the inverse pace at a point in time and space: 1/(dt/dx) ≈ dx/dt(x).

The (time) velocity of a body is the displacement traversed per unit of independent time, Δx/t. The instantaneous velocity is the time velocity at a point in space and time: dx(t)/dt. It is the reciprocal of the puncstanceous lenticity: 1/(dt/dx(t)).

The inverse velocity (time lenticity) of a body is the reciprocal of the velocity, 1/(Δx/t) ≈ Δtx. The instantaneous lenticity is the lenticity at a point in space and time: 1/(dx(t)/dt) ≈ dt/dx(t). It is the reciprocal of the instantaneous velocity: dx(t)/dt.

The (space) lenticity of a body is the dischronment per unit of independent length, Δt(x)/x. The puncstanceous lenticity is the time lenticity at a point in time and space: dt(x)/dx.

The inverse lenticity (space velocity) of a body is the reciprocal of the lenticity, 1/(Δt(x)/) ≈ Δxt(x). The puncstanceous velocity is the lenticity at a point in time and space: dx/dt(x).

Addition of speeds or velocities is with arithmetic addition (+) since the time interval in the denominator is the same for all.

Addition of inverse speeds or inverse velocities is with reciprocal addition (⊞) since the space interval in the numerator is the same for all.

Addition of paces or lenticities is with arithmetic addition (+) since the space interval in the denominator is the same for all.

Addition of inverse paces or inverse lenticities is with reciprocal addition (⊞) since the time interval in the numerator is the same for all.