At its very simplest motion is Uniform Motion. Uniform motion is motion with constant momentum. To view simple uniform motion in terms of its momentum... think this way.
Valentino's Wake
From 1920 through 1934, Rudolph Valentino, starred as a dashing hero in over a hundred silent screen movies. But in 1936, at the peak of his popularity, he died. At his wake his body was displayed in an open casket. One newspaper asserted:
"Today 9,000 persons per hour passed
Valentino's casket in solemn tribute."
Is that possible? Could 9,000 people have walked past his casket in an hour? Make some assumptions and prove it is possible or it is impossible.
♦ While it cannot be determined if this happened, it can be determined if this did not happen. A newspaper photo showed there were four lines of viewers. With reasonable assumptions, we can determine, approximately, how many persons might have walked past the coffin in similar circumstances.
The line will move with uniform motion. Our system will be a person, that very last person in line who moves uniformly and will be the last person to view Valentio in one hour hence. We label the person "Last." The position of that last mourner, at the start and for all time within the hour is:
PLast(t) = PLast, 0+ + VLast t
Walking in procession, we estimate each mourner would move about 1.5 feet per second toward the casket.
PLast(t) = PLast, 0+ + (1.5 ft/s I) t
Mourners are people and when people walk in a line, they maintain space between themselves. We estimate each person would occupy about five feet of space, of length of the procession line.
Thus the position of our "Last" person in linme at the start (at t = 0+) would be 5N feet away from the casket, where the letter "N" represents the number of persons ahead of our "last" person.
PLast, t = 0+ = 5N (- I)
Use the above fact to update the first equation.
PLast(t) = - 5N I + (1.5 ft/s I) t
This is a good place to explain the meaning of "time equals zero, (t = 0)" and "time equals zero plus, (t = 0+)." Both times are the same time. Zero means zero and the "plus" means a very, very short time later. The purpose of the distinction is to emphasize the beginning nature of an event. When, if ever was time zero. Yet we use the idea "time equals zero" to designate beginning. A close word is epoch. Our usage is: t = 0 before an event (nothing happening) and the event commences at t = 0+. Both times are zero, one with nothing happening, no clock running, the other stsrt-time is part of the time of the physical event.
In an hour, according to our uniform motion model, our mourner named "Last" will be beside the casket, that is standing at the origin (position zero) with time equal to one hour (t = 0+ + 3600s). We apply these numbers:
0 = 5ft N(- I) + (1.5 ft/s I) (3600s/hr)(1 hr) or N = 1080
But the photograph showed four lines of mourners. Thus, by our estimate, a maximum of (4 x 1080) 4320 mourners could pass the casket. Our assumptions are reasonable; we conclude the reported number, 9000, is wrong.