Miragememories said:
My statements were directed to people in the world that understand that when an object is not moving, it has no velocity or acceleration.
Ok, when you throw the ball up in the air at every instant it feels the attraction of gravity wanting to pull it back down. The attraction is expressed as the force
F=GmM/r^2, where
G is a constant,
m is the mass of the ball,
M is the mass of the earth, and
r is the distance center-to-center from earth to ball. Inserting the approximate values for earth's mass and radius, and the constant,
GM/r^2 ~ 32.2 ft/s^2 = g, or
9.81 m/s^2 = g in metric. While the ball is in motion, neglecting air resistance, this is the only force acting on it.
Newton's second law tells us that the sum of the forces acting on the object is equal to the mass of the object times its acceleration,
F = ma. So on the left we have only the force
F=mg described in the paragraph above. On the right we have
ma. That gives us:
mg = ma
Now clearly this is true at all times during the flight of the ball, since the gravitational force is always acting. Even when the ball comes to a stop at the top. If the acceleration were somehow zero (
a=0) at the top, we would have
mg = 0. There would suddenly be no gravitational attraction acting on the ball. No net forces at all. This presents a problem, because Newton's first law tells us that if there are no net forces acting on the object that it continues its motion at constant velocity or remains at rest. Since the ball is "at rest" at the top of its flight, it would thus remain so. If it is not your personal experience that objects remain hanging in the air once you have thrown them up, then you must accept that the sum of the forces is not zero, and thus
ma must have some value, as we have shown that
a must be equal to
g.