One Motion, Three Movies

You'll learnto convert a velocity between reference frames using object-first, frame-second subscript bookkeeping.

Two trains roll past a platform — and every observer films a different set of numbers, all of them correct. Learn the two-subscript bookkeeping that converts between frames, take it into 2D with a swimmer in a current, then differentiate the whole transformation and watch acceleration come out identical for every inertial observer.

8 STEPS · 6 QUICK CHECKS · v3

FRAME LAB

Before you start

What you're looking at

Two trains passing a station platform: Train A at +20î m/s and Train B at +25î m/s, both measured from the platform.

The question

How fast is Train B actually moving?

Watch for

The fine print — those numbers were measured by the platform; passengers inside Train A get a different, equally correct answer.

What the symbols mean

Subscripts read object first, frame second (vB,P is velocity of B relative to platform); î is the +x direction; units m/s.

Step 1 / 8