# My speed?

1. Jan 17, 2009

### Sriram.S

What speed am I traveling at when I am run at the top a moving train.(Assuming train is going at 10 km/hr and I am running at 2km/hr)

Sriram

2. Jan 17, 2009

### HallsofIvy

Classical Physics:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is 10+2= 12 km/hr. If you are running toward the back of the train, your speed relative to the ground is 10-2= 8 km/hr.

Relativity:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is $(10+2)/(1+ (10)(2)/c^2$= $(10+2)/(1+ 20/( 299,792,458)^2$ which, even to 12 decimal place accuracy, the limit of my calculator, 12.000000000000 km/hr. Similarly, if you are running toward the back of the train, your speed is still 8 km/hr to with 12 decimal places.

Those speeds are simply to low for relativistic effects to be measurable.

3. Jan 17, 2009

### Rajini

3.33 m/s [for stationary observer in ground]

4. Jan 17, 2009

### Fredrik

Staff Emeritus
Microsoft PowerToy Calculator for Windows XP says 11.999999999999999258233295964254424402093624772443805600625656194569150201085437567008465314216160709462212415964961122075175062

By the way, that has to be the slowest runner ever, considering that normal walking speed is about 6 km/h.

5. Jan 17, 2009

### HallsofIvy

Hey, YOU try running on top of a moving train!

6. Jan 20, 2009

### Tac-Tics

You're at rest. You are always at rest relative to yourself.