2.2 2.3 Calc-based Physics - Free-fall no ex
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2.2-2.3 Calculus-based Physics: Free-fall
Formula
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
Notation:
• Position Function: s(t)• Velocity Function: v(t)• Acceleration Function: a(t)
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)
The Calculus...
s(t)
v(t) = s’(t)
a(t) = v’(t) = s”(t)
Position Free-fall Formula (within a body’s gravitational field)
212( ) o os t gt v t s
initial velocityov
initial positionos
2 2
gravitational constant
( 32 ft/sec 9.8 /sec on Earth)
g
or m