When air resistance can be left out, gravity is the only force acting on a falling body. The acceleration then points downward and its size is fixed at . Taking upward as positive, .
What matters is that this value does not depend on the body. Drop a heavy ball and a light one together from the same height and they are level with each other at every instant, and they land together. That is why the two arrows in the figure have the same length.
Heavy things seem as though they ought to fall faster only because we normally watch air resistance along with gravity. A feather and an iron ball part company because of the air, not because of their weight.
Let go quietly and the motion is uniform acceleration with an initial speed of zero. This is called free fall.
Set in the position formula and the first term disappears, leaving the distance fallen as . The speed is .
Double the time and the speed doubles, but the distance fallen becomes four times as great. Only the distance carries the square, so the stamped dots spread wider and wider the farther down they go.
Throw the ball straight up and gravity is still the only force acting. The acceleration therefore points downward the whole way, on the rise as much as on the fall.
At the highest point the velocity is zero, and in the figure the velocity arrow is the one that vanishes. The acceleration arrow remains, at exactly the same length. So the ball does not stay up there. It begins to fall at once.
The height of that point comes from the equation with the time removed. Putting into gives . Here too a square appears. Throw twice as fast and the ball rises four times as high.
On the velocity graph, the rise and the fall are one straight line. It neither bends nor breaks. The crossing of the zero line is the highest point, and on either side of it the motion is a mirror image.
The area enclosed by the line and the time axis is the height gained above and the height lost below. The ball returns to the ground it left, so the two areas are equal, and the time going up equals the time coming down.
At any given height the speed is the same on the way up as on the way down. Only the direction is reversed. shows why: enters squared, so the equation fixes the speed alone and says nothing about which way the ball is going.
There is no need to learn the throw upward and the free fall as two separate motions. They are one and the same uniform acceleration, differing only in the sign of the initial velocity.