Contextual Applications of Differentiation Vocab and Volume Formulas

Position

Where a particle is located at a given time, t. (a.k.a. s(t))

Velocity

Rate of change of a position (a.k.a. v(t))

Acceleration

rate of change of velocity (a.k.a. a(t))

Free Fall Motion

d = 1/2 g t^2

Direction changes

When velocity changes from pos. to neg. or neg. to pos at a point (time). Doesn't need to be defined or pass through zero to change direction.

Gravitational constant

9.8m/s^2

Circumference Formula

2πr or πd

Area of a Circle

=πr²

Volume of a cylinder

=πr²h

Volume of a cone

=1/3πr²h

Volume of a sphere

=4/3πr³

Surface Area of a Cylinder

=2πr²+2πrh (m²)

Surface Area of a rectangular prism

=2lw+2lh+2wh (m²)

Volume of a rectangular prism

=lwh

Pythagorean Theorem

a²+b²=c²

What is added when taking the derivative of

Surface Area, Volume, etc.

d(x)/dt

Derivative of Position

velocity, d(v)/dt

Derivative of Velocity

acceleration, a(t),

Order of acceleration derivatives

a(t)=v'(t)=s''(t)

Area of a triangle

A=1/2bh

Volume of a triangular prism

V=(1/2bh) (h or l)