The *arc length* of a motion is the length along the curve it traces out. The *arc time* of a motion is the travel time along the route it traces out.

The *time rate* is “The rate at which something takes place over time.” The *space rate* is the rate at which something takes time over a route.

A quantity at an instant of time is *instantaneous*. A quantity at a point in space is *punctaneous*, from Latin *punct*(us) + (instant)*aneous*.

*Speed* is the time rate of motion, the arc length per unit of arc time. The speed at an instant of time is called the *instantaneous* speed, which equals the differential arc length per differential arc time or the magnitude of the instantaneous velocity.

*Pace* is the space rate of motion, the arc time per unit of arc length. The pace at a point of space is called the *punctaneous* pace, which equals the differential arc length per differential arc time or the magnitude of the punctaneous progressity. A gradient is the space rate of change of a function or scalar field.

*Displacement* is the directed distance or vector difference between two points in three-dimensional space. *Distimement* is the directed duration or vector difference between two instants in three-dimensional time.

*Velocity* is the time rate of change of distimement, which consists of the speed and direction of motion. The average velocity is the displacement per arc time of motion. The velocity at an instant of time is called the *instantaneous* velocity, and is the differential displacement per differential arc time. The instantaneous velocity equals the time rate of change of the displacement.

*Progressity* is the space rate of change of distimement, which consists of the pace and direction of motion. Progressity is the rate of progress toward a destination. The average progressity is the distimement per arc length of motion. The progressity at a point of space is called the *punctaneous* progressity, and is the differential distimement per differential arc length. *Progressity* is from *progress* + *ity* (cf. velocity).

*Acceleration* is the time rate of change of velocity. *Prestination* is the space rate of change of progressity.

The first moment of mass is mass times distance. The *momentum* is the time rate of change of the first moment of mass. The first moment of vass is vass times duration. The space rate of change of the first moment of vass is the *climentum*, from Latin *clim*(a), slope + (mom)*entum*.

*Power* is the time rate of change of energy. *Force* is the space rate of change of energy.