Well, I don’t really know if it’s a math problem. Maybe physics.

Anyway, I pulled to a railroad crossing just as the lights began flashing and the gates went down. The three engines when WHOOSHING by. My minivan shook.

The cars following the engines were mostly empty; that is, the flats where containers are stacked were empty. What I’m getting at is that they’re really light. Lighter than empty boxcars.

So I sit singing along to the radio watching the train go by, the container flats start to be filled with containers. First one layer, then two layers.

At the same time, the train seems to be slowing down. At first I assumed that this was simply what was happening. Then I made the connection between slower train and heavier cars.

Which led me, who is math/science impaired, to wonder if the WHOLE train had slowed, or just the cars in the latter part, which was heavier. Is it possible for two parts of a train to get traveling at different rates of speed? Would it depend on how long the train was? This one was fairly long.

If this is impossible, was it just coincidence that the train slowed just as I observed its load was heavier?

If two parts of a train travel at different rates of speed, then it will either crash or separate.
(It’s tricky to see what would make a train do this. All the energy comes from the engine, and the rest of the train is just pulled along.)

If this is impossible, was it just coincidence that the train slowed just as I observed its load was heavier?

Just a coincidence. The train couplings are basically solid, so the whole train is forced to go the same speed.

Of course, there is some flexibility in the couplings, and in the atomic bonds of the steel. So an extremely long train could conceivably have some small variations in the exact speed of its components, but it would be small. Unless the train was half a light-year long.

but the different parts of the train can go at different rates. They have to.

Take a train at rest. First the engine starts moving before the rest of the train, as the miniscule amounts of slack in the couplings is taken up. Then each car in turn starts moving.

So yes, the different parts of the train can move at slightly different speeds at any given moment. This is instantaneous speed.

The average speed over a given distance will also be different per car, but also very slightly.

For example, the engine may go exactly 30 miles in 45 minutes, but the caboose (if they still exist ) will take 45 minutes, 0.1 seconds to travel exactly 30 miles from its starting position.

But there won’t be any noticable speed difference. If the last car is going 30 MPH, the engine is also going 30 MPH, + a fractional mile per hour.