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