Concept preview

What you will be able to do

1. 01Understand that velocity depends on the observer's frame of reference
2. 02Combine velocities using vector addition
3. 03Solve river-crossing and aircraft-in-wind problems

When you walk down the aisle of a moving train, how fast are you going? It depends on who is watching. To a passenger you stroll at $1\ \text{m/s}$; to someone on the platform you rush past at $1$ plus the train's speed. Neither answer is wrong — velocity has no meaning until you name the frame of reference it is measured in. This is the heart of relative motion, and it is measured with subscripts that keep track of what, relative to what.