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# Is average speed the magnitude of average velocity?

Updated: 10/17/2022

Teea

Lvl 1
10y ago

No. The average speed is the average of the magnitude of the velocity but not the magnitude of the average of the velocity.

This is because for vectors |A + B| ≤ |A| + |B|.

Suppose you travel 100 metres due East at 10 metres per second and then 100 metres due North also at 10 metres per second. Your speed, throughout, is 10 metres per second and so that is your average speed.

But your average velocity is the total displacement vector divided by the total time. This is

100*sqrt(2) metres due NE/20 sec = 7.07 metres per second due North East.

Its magnitude is 7.07 metres/sec.

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10y ago

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