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It doesn't need to "remember" that you pushed it; conservation of energy is what says that it must move if pushed. Here's another way of thinking of it: if an atom is not being accelerated from behind, not being slowed down from the front, and not being pushed from either side, then it's only logical that it will maintain its current momentum (whether that moment is zero or very large). If the atom "forgot" that you pushed it and slowed down, that would be equivalent to a force acting on it to slow it down. If no such forces are present, then it will not slow down.
Well, yes, but that doesn't really explain why it doesn't stop moving as soon as you stop pushing it.
Staying in uniform movement is the same as staying still and requires no force
ARTICLE XLI.—THE FIRST LAW OF MOTION.Law I.—Every body perseveres in its state of rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces. The experimental argument for the truth of this law is, that in every case in which we find an alteration of the state of motion of a body, we can trace this alteration to some action between that body and another, that is to say, to an external force. The existence of this action is indicated by its effect on the other body when the motion of that body can be observed. Thus the motion of a cannon ball is retarded, but this arises from an action between the projectile and the air which surrounds it, whereby the ball experiences a force in the direction opposite to its relative motion, while the air, pushed forward by an equal force, is itself set in motion, and constitutes what is called the wind of the cannon ball.But our conviction of the truth of this law may be greatly strengthened by considering what is involved in a denial of it. Given a body in motion. At a given instant let it be left to itself and not acted on by any force. What will happen? According to Newton's law it will persevere in moving uniformly in a straight line, that is, its velocity will remain constant both in direction and magnitude.If the velocity does not remain constant let us suppose it to vary. The change of velocity, as we saw in Article XXXI., must have a definite direction and magnitude. By the maxim of Article XIX. this variation must be the same whatever be the time or place of the experiment. The direction of the change of motion must therefore be determined either by the direction of the motion itself, or by some direction fixed in the body.Let us, in the first place, suppose the law to be that the velocity diminishes at a certain rate, which for the sake of the argument we may suppose so slow that by no experiments on moving bodies could we have detected the diminution of velocity in hundreds of years.The velocity referred to in this hypothetical law can only be the velocity referred to a point absolutely at rest. For if it is a relative velocity its direction as well as its magnitude depends on the velocity of the point of reference.If, when referred to a certain point, the body appears to be moving northward with diminishing velocity, we have only to refer it to another point moving northward with a uniform velocity greater than that of the body, and it will appear to be moving southward with increasing velocity.Hence the hypothetical law is without meaning, unless we admit the possibility of defining absolute rest and absolute velocity.Even if we admit this as a possibility, the hypothetical law, if found to be true, might be interpreted, not as a contradiction of Newton's law, but as evidence of the resisting action of some medium in space.To take another case. Suppose the law to be that a body, not acted on by any force, ceases at once to move. This is not only contradicted by experience, but it leads to a definition of absolute rest as the state which a body assumes as soon as it is freed from the action of external forces.It may thus be shown that the denial of Newton's law is in contradiction to the only system of consistent doctrine about space and time which the human mind has been able to form.