Question

explain the meaning of p=mv where symbols have their usual meaning

Answer 1

p = momentum
m= mass
v = velocity

Answer 2

We can certainly define some other operation, such as division, and say p = m/j where j is the rate of change of time relative to position. It is just easier for humans to think in terms of velocity (v) which is the rate of change of position with time. As others have said, physicists are interested in describing the physical world so the quantities that we are interested in must describe something that has some physical significance. Newton observed that the same force applied for same time to objects of different mass resulted in the same change in the quantity of motion for each. 'Quantity of motion' was the term Newton used for the product of velocity and mass. So, Newton concluded that keeping track of this quantity of motion, which we now call p = mv would be very useful.
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