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
Jerk (physics) Jerk (physics) In physics, jerk is the rate of change of acceleration; that is, the time derivative of acceleration, and as such the second derivative of velocity, or the third time derivative of position. According to the result of dimensional analysis of jerk, [length/time], the SI units for its magnitude are m/s (or m⋅s); this can also be expressed in standard gravity per second ("g"/s). Jerk is a vector, and (as with "acceleration") there is no distinct term to denote its scalar magnitude (more precisely, its norm, as, e.g., there is "speed" for the norm of the velocity vector). Jerk