Relative Motion
Keep one physical event fixed and change the observer who measures it.
A passenger walks west down a train aisle while the train moves east. Which way is the passenger moving?
Do not answer with a formula yet. Use the frame switch below. The passenger and train do not physically change when you switch observers, but the measured velocities do.
Switch observers. Keep the event.
Velocity is not owned by the object alone. It describes an object relative to a chosen frame.
A walker can move west relative to the train and east relative to the ground at the same instant. Nothing contradictory happened. The two observers used different reference frames.
For ordinary low-speed motion, compatible relative velocities form a signed chain. Direction matters, so choosing a positive direction turns the physical story into arithmetic.
Read each subscript as “first object relative to second.” The middle reference, T, links the two measurements.
A direction and speed are incomplete until the observer or reference frame is understood.
Choose a positive direction, keep the signs, and add compatible relative velocities in ordinary mechanics.
An object can be stationary in one frame and moving in another without changing the physical event.
Changing reference frames does not add a new force.
In this constant-velocity example, switching from ground to train coordinates changes measured position and velocity, not the underlying interactions. Reference frame and physical cause are different questions.
If east is positive, westward velocities are negative. Reversing the sign convention changes every relevant sign consistently, not the physical answer.
A train moves east at 6 m/s. Set the passenger's walking velocity so a ground observer sees the passenger momentarily at rest.
East is positive. Adjust the walker/train velocity until the ground velocity reaches zero, then lock your choice.