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Acceleration is a change in speed or direction. Acceleration like most variables in science is a quaternion, consisting of a real part and a vector part, a=ar + av.Unfortunately, our education system has not caught up to this fact and most students don't get to study vectors and hardly any get to study quaternions. An example of the real and vector acceleration is given in Gravity.

The gravitational energy is E=-GmM/r + mcV= -mu/r + mcV, the force of gravity is

F=(mv^2/r - mcv/r cos(x)) + (dmcV/cdt + Del x mcV - Del mu/r).

The acceleration is:

a= f/m= (v^2/r -cv/r cos(x)) + (dV/dt + cv/r sin(x)T' + v^2/r R/r)

The first parenthesis gives the real part of acceleration and the second parenthesis gives the vector part of acceleration. V^2/r is the centripetal acceleration and -cv/r cos(x) is the centrifugal acceleration.

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