In math, you say: velocity is the rate of change of position with respect to time.
I'm looking for a better, mathematically correct way to say that, without using the phrase with respect to and velocity is the time-derivative of position.
I would just say over:
An object's velocity is the change in its position over time.
Which is a natural expression of the derivative dx/dt.
Well, you could say "with relation to" or in some cases "as a function of". I'm not quite sure what's wrong with "with respect to" in this case, though.
Velocity is the rate of change of position with time.
An object's velocity is the amount by which its position changes in a given time.
I would say velocity is the rate at which an object moves, or velocity is the measurement of the rate and direction of change in position of an object.
Ok how about as?
Velocity is the rate of change of distance AS TIME changes.
Say we have the volume of a cone
Then say we take the partial derivative with respect to cone radius.
Then we could say the rate of change of that volume AS radius changes, is that equation.