Speed and reference frame: practical application

Speed also depends on the frame of reference

The speed of an object is measured as the distance travelled per unit of time: v = d / t (in m/s or km/h). Like motion, it depends entirely on the chosen frame of reference.

Example: a passenger walking in a train

A passenger is walking towards the front of the train at 5 km/h. The train is travelling at 100 km/h relative to the ground.

Reference frame	Passenger’s speed
Train’s reference frame	5 km/h
Earth’s reference frame (ground)	100 + 5 = 105 km/h

If the passenger were walking towards the rear of the train at the same speed, then, in the Earth’s reference frame, the speed would be: 100 – 5 = 95 km/h.

How do you choose the right reference frame?

You choose the reference frame depending on the question being asked:

• To study passenger comfort inside an aeroplane -> the aeroplane’s reference frame.
• To study the trajectory of an aeroplane over continents -> the Earth-centred reference frame.
• To study the Moon’s motion around the Earth -> the geocentric reference frame.

There is no single ‘correct’ reference frame: there is a reference frame that is appropriate for the problem being studied.

A common pitfall to avoid

Do not confuse ‘at rest’ with ‘having no velocity at all’. An object that is at rest in one reference frame may have a very high velocity in another reference frame (for example, you are at rest relative to your chair, but you are moving at over 1,600 km/h with the Earth’s rotation, in the geocentric reference frame!). Always specify the reference frame before giving a velocity value.