v = v0 + a ∆t ∆x = v0∆t + 1/2 a∆t2 v2 = v02 + 2a∆x

To create equations for freely falling bodies, simply replace a with g.

v = v0 + a ∆t ∆x = v0∆t + 1/2 a∆t2 v2 = v02 + 2a∆x

v = v0 + g ∆t ∆x = v0∆t + 1/2 g∆t2 v2 = v02 + 2g∆x

When freely falling bodies start from rest, v0 = 0, so: v = g ∆t ∆x = 1/2 g∆t2 v2 = 2g∆x

These equations refer to a situation with constant acceleration due to gravity and no air resistance. Such motion is called free fall.

Example: A ball is dropped froma height of 10 meters Example: A ball is dropped froma height of 10 meters. How long will it be in the air before it strikes the floor?

Example: A ball is thrown vertically upward with a velocity of 100 m/s Example: A ball is thrown vertically upward with a velocity of 100 m/s. (a) To what height will it rise? (b) How long will it take for the ball to fall back to the earth?

Example: A ball drops from rest and attains a velocity of 62 m/s Example: A ball drops from rest and attains a velocity of 62 m/s. How much time has elapsed?

Example: How far did the ball in the previous problem fall during the third second?