Question

Newton used the phrase “quantity of motion” for ?

Answer 1

Hint:Here we will first see the history of the word motion, how motion is related to mass, and lastly we will know which quantity Newton referred to as “quantity of motion”.The term "motion" was used in ancient times – and still is in some contexts today – to refer to a strictly kinematic characteristic of a physical body, quantified by the parameter v, which represents the distance travelled per unit time.

Complete answer:
 Of course, distance and time are not trivial concepts in and of themselves, leading to conundrums like those described by Zeno, but most people in ancient times considered the kinematic principle of motion satisfactory and unproblematic.

The modern science of dynamics, on the other hand, was founded on a fundamentally different conception of how to measure “motion.” After defining “quantity of matter” as the product of density and volume at the start of the Principia, Newton suggested the following definition: the measure of motion is the quantity of motion, which is derived from both the velocity and the quantity of matter.

In other words, Newton defined the quantity of motion of a given object as the product mv, where m is the mass of the object, rather than simply the kinematic velocity v of the object. This is a huge shift in the way we think of motion, from a kinematical to a dynamical perspective. It means that “motion” without mass (or, as we now say, mass-energy) is unlikely, implying that the strictly kinematic definition of motion is meaningless and that mass is a scale factor on the spatio-temporal parameter $v$.

Note: Newton's description implicitly regarded the parameter v as the scalar speed, rather than the vector velocity, since the quantity (singular) of motion is a scalar. As a result, the quantity of motion differs from the modern definition of momentum, which is a vector.