1. May 31, 2007

### JustinTime

In Max Born's Einstein's Relativity he has a part called "The Study of Motion--Rectilinear Motion He says that velocity has the dimension length divided by time (v=l/t). At one point he talks about a line on an xy plane curving, and says its motion is continually changing. To measure its exact velocity differential calculus is needed. "It is sufficient for us to imagine the continuous curve replaced by a polygon whose straight sides represent uniform motions with definite velocities. The bends of the polygon (that is, the sudden changes of velocity) may be supposed to succeed each other at equal intervals of time, say T=1/n" What I'm trying to type is T equals 1 divided by n. He uses a small capital (greek?) "T" which I understand to mean a small interval of time. Does the "1" represent one bend? What does "n" represent?

He later says "let each such change of velocity have the value w; then if there are n per sec. the total change of velocity per sec is nw per sec = w/t = b" The second part of my question is why is the change of velocity represented as "n" times "w" (nw) ?

Thanks,
JustinTime

2. May 31, 2007

### MaWM

n is just the number of subdivisions in a second. If there are n subdivisions in a second, then each subdivision is T=1/n long. If the change in velocity per subdivision is w, the the change in velocity per second is that times the number of subdivisions in a second. wn.

3. May 31, 2007

### JustinTime

Got it. Thank you!