1.6: Free fall: a special case of constant acceleration

Key idea:  Free fall is constant acceleration.  All of the equations that we just learned will work with free fall.

Textbook Section: 2-8

An object is in free fall if it is being accelerated only by gravity.  That is, we are assuming that there is no air resistance preventing the object from experiencing the full acceleration of gravity.

All of our equations still work, but we're going to make some variable changes.  (Do you sense a theme here?)

• First, because the acceleration is gravity, we will replace the letter a with the letter g.

• Second, because the motion is vertical, we will use y as our position variable, not x.  We will use vy as our velocity variable.

• Third, because gravity accelerates objects in a downward direction, we will put a negative sign in front of the letter g to indicate that direction.

Our equations become:

Pause and make sure you can do the math and get the same results!!  If you have any questions, put them in the section discussion below.

Big, important observation:  We now have two sets of equations of motion.  One uses the letter x and refers to horizontal motion.  The other uses the letter y and refers to vertical motion.  This is a clue as to how we will handle motion in two dimensions, which is the next module of the course.

Pro tip:  Don't cheat and use x for everything.  Trust me, you really need to keep horizontal and vertical motions separate.

A couple of random things that will make your (homework) life much easier:

• If an object is "dropped" its initial velocity is zero.

• When an object reaches its maximum height, the final velocity (at the top) is zero for an instant.

• On earth, g = 9.8 m/s2.  Note that g is not negative.  We put a negative sign in front of it in the equations instead.

• Free fall is one of those areas where positive and negative signs become very important.  A downward displacement or velocity or acceleration will have a negative sign!