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According to my book, during uniform circular motion, the acceleration is

a= v^2/r

where v is the speed at which the object is moving and r is the radius of the circle.

However, this formula is not treating acceleration as a vector because the result of this formula is a scalar while acceleration is a vector. I think that this formula refers to the modulus of the acceleration vector. I'd like to know an explanation about how calculations could be made while treating acceleration and velocity as vectors. i.e. calculating the acceleration vector in a moment t. As acceleration is changing, is there jerk? Were there any, what would it be?