Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Power (physics) yields: where "A" and "B" are the beginning and end of the path along which the work was done. The power at any point along the curve "C" is the time derivative In one dimension, this can be simplified to: In rotational systems, power is the product of the torque τ and angular velocity ω, where ω measured in radians per second. The formula_13 represents scalar product. In fluid power systems such as hydraulic actuators, power is given by where "p" is pressure in pascals, or N/m and "Q" is volumetric flow rate in m/s in SI units. If a