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Well if you are familiar with calculus the projection of acceleration vector a(t)on to the Tangent unit vector T(t), that is tangential acceleration. While the projection of acceleration vector a(t) on to the normal vector is the normal acceleration vector.

Therefore we know that acceleration is on the same plane as T(t) and N(t). So component of acceleration for tangent vector is (v dot a)/ magnitude of v

component of acceleration for normal vector is

sqrt((magnitude of acceleration)^2 - (component of acceleration for tangent vector)^2)

sorry i can't explain it to you more cause I don't have mathematical symbols to work with

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Q: What are the tangential and normal components of acceleration?
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