Free fall and vertical motion under gravity

Near the earth's surface, with air resistance neglected, every body has the same downward acceleration g ≈ 9.8 m s⁻², whatever its mass.

If upward is taken positive, a = −g throughout the flight, on the way up, at the top and on the way down.

A body released from rest falls a distance ½gt² in time t, and its speed after falling a height h is √(2gh).

A body thrown up with speed u rises to a height u²/2g in time u/g; with no air resistance it takes the same time to come down to the launch level and returns with the same speed.

When a body is thrown up from a height above the ground, use one equation from launch to landing with the landing displacement taken as negative; there is no need to split the flight.

Galileo's law of odd numbers: for a body starting from rest with constant acceleration, distances covered in successive equal time intervals are in the ratio 1 : 3 : 5 : 7 and so on.

In free fall, v plotted against t is a straight line with slope −g (upward positive), while x plotted against t is a parabola.