# Train kept a-rollin'

Gold Member
My friend was in a ponderous mood and asked me the following question:

If a train is traveling at 40mph and you are inside the train and running 10mph in the same direction as the train is travelling, what speed are you moving at?

The answer i gave him was that

1/ The overall system is traveling at 40mph
2/ You are running at 10mph inside the train
3/ To an outside observer you appear to be running at 50mph

Was i right in my assumptions?

Thanx

Staff Emeritus
Gold Member
You are correct. The critical point is that you have to define your "frame of reference" before you can give a velocity.

All of the following are correct:

The person is running at 10 mph to an observer sitting on a seat on the train.

The person is running at 50 mph to an observer sitting still beside the railroad track.

The person is running at 0 mph to an observer who is running along with him.

- Warren

Gold Member
Ok that's cool then, glad i was right for once

If the train were to travel at 40mph and you were inside the train running 10mph in the opposite direction, what would observers view?

Am i right in assuming that again,

1/ The system is moving at +40mph
2/ You are running at -10mph to an inside observer
3/ To an outside observer you are facing the wrong way traveling at +30mph

Thanx
[?]

Staff Emeritus
Gold Member
That is also correct. In general, you'll make your life easier if you never refer to velocities without mentioning the reference to which those velocities are measured.

The system is moving at +40mph

Say

The system is moving at +40mph to an observer at rest on the ground.

- Warren

Gold Member
Yeah thanks i was just thinking simple terms, my friend isn't the sciency type so its best not to confuse him!