To understand how things fall, we need to look at a few important ideas:

1. Acceleration: When an object falls, it speeds up at a steady rate because of gravity. We call this rate $g$, and it’s about 9.81 meters per second squared ($9.81 \, \text{m/s}^2$).

2. Equations of Motion: There are three main formulas that we can use for objects that are falling:

   • 1st Equation: $v = u + at$
   • 2nd Equation: $s = ut + \frac{1}{2} a t^2$
   • 3rd Equation: $v^2 = u^2 + 2as$

3. Variables: Here are what the symbols in the formulas mean:

   • $u$ = starting speed (initial velocity)
   • $v$ = speed at the end (final velocity)
   • $a$ = acceleration (which is gravity, $g$)
   • $s$ = how far it has fallen (distance fallen)
   • $t$ = how long it has been falling (time taken)

4. Application: We can use these formulas to figure out where the object is, how fast it is going, and how long it takes to fall when gravity is pulling it down.