Vector Calculus 19: Derivative of a Constant-Length Vector

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Since at any one instance, a particle's velocity is always just some number, wouldn't that mean that its acceleration would be the sum of two derivatives, i.e. the derivative tangent to the curve plus the derivative orthogonal to the curve? And the vector that results from the sum of these two derivatives would be the overall acceleration?

Phi
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Why did you draw a vector function of constant length as a wave? Shouldn't it be circular? (Shouldn't we always take a common origin for the changing vector?)

sathyaperla
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oh hi Dr, I have another question, what is the derivative of a constant scaler with respect to a vector variable?

eddiechen