Visual physics derivation! (Centripetal acceleration)

The most logical explanation for why centripetal acceleration formula has a v^2/R.
The centripetal force given by mv^2/R appears in most places in mechanics. However, it's not very straight forward as to why the equation has a speed squared in it, or why it's inversely proportional to the radius of the turn. In this animated video, we will get the intuition behind this.
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Music Attributions:

1. Legend of One by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/...

Source: http://incompetech.com/music/royalty-...

Artist: http://incompetech.com/
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2. Hypnothis by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/...

Source: http://incompetech.com/music/royalty-...

Artist: http://incompetech.com/
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Chapters
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00:00 Visualising change in velocity
01:00 Doubling speed
03:40 Tripling speed
05:00 Why V^2
05:25 Doubling radius
07:25 Tripling radius
08:03 Why 1/R