1. 2.2-2.3
Calculus-based
Physics: Free-fall
Formula

2. Vocabulary
• Position: the location of a body at a particular time (t)
• Displacement: the change in position of a body (how far
it is from its starting point)
• Velocity: the rate of change of position with respect to
time
* instantaneous velocity = derivative
* average velocity = algebraic slope
• Speed: the absolute value of velocity
• Acceleration: the rate of change of velocity with respect
to time

3. Notation:
• Position Function: s(t)
• Velocity Function: v(t)
• Acceleration Function: a(t)

4. Units:
• Position: linear units (e.g. m)
• Velocity: linear unit per unit of time
(e.g. m/s)
• Acceleration: unit of velocity per unit
of time (e.g. m/s/s or m/s2)

5. The Calculus...
s(t)
v(t) = s’(t)
a(t) = v’(t) = s”(t)

6. Position Free-fall Formula
(within a body’s gravitational field)
1 2
s(t) 2 gt vot so
vo initial velocity
so initial position
g gravitational constant
( 32 ft/sec2 or 9.8 m /sec2 on Earth)