# If you travel around the world, what would the velocity be?

This isn't a homework question. My friend stumbled upon his textbook that stated since the circumference of the globe is 2*pi*r, the velocity of someone who "ran all the way around" would be v = (2*pi*r)/t.

However, isn't the displacement zero? And velocity = displacement/time?

so is this a textbook typo, or is there another point I'm missing? xD

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displacement is a vector quantity so it is linear, the displacement would be the whole circumference of the earth, as it is a vector quantity ;)

Last edited:
jtbell
Mentor
The average velocity for a complete circumnavigation is zero.

The instantaneous velocity at any point in the trip has a magnitude 2πr/T, assuming constant speed, and a direction which is continuously changing.

No, displacement is a vector quantity.
Distance is scalar

Many things here. First displacement is a vector quantity and so is velocity. The equation,

velocity = displacement/time

is a vectpr equation, describing the AVERAGE velocity.

If you travel around the world, starting and ending at the same location, at a constant speed, your average velocity is zero because during half the travel, the direction of your velocity vector is one way. During the other half of the travel, it's direction is the opposite way.

Since you are moving at constant speed, the AVERAGE speed, defined as
speed = distance/time (which is also the only speed you travel at) will be

2*pi*r/t

By the way, do we consider a geodesic or straight line displacement (which actually is the shortest distance between these two points!) in this case, for the displacement vector?

Eg, if we travel halfway across the globe, would our displacement be the diameter of the Earth or will it be equal to $\Pi$r ?

By the way, do we consider a geodesic or straight line displacement (which actually is the shortest distance between these two points!) in this case, for the displacement vector?

Eg, if we travel halfway across the globe, would our displacement be the diameter of the Earth or will it be equal to Πr ?
I would say the diameter would be the displacement in this case.

jtbell
Mentor
Displacement is the length of a straight-line path between the start and end points (2r in this case).

Distance is the length along the path traveled (πr in this case).