Motion Fill-in-the-blank

The derivatives of a particle’s position is

velocity

The second derivative of a particle’s position is

acceleration

A derivative of a particle’s velocity is

acceleration

speed is defined as

absolute value of velocity

Average velocity is calculate by doing slope with

position [x(b)-x(a)/b-a]

average acceleration is calculatedd by doing slope with

velocity [v(b)-v(a)/b-a]

a particle is at rest when

v(t) = 0

A particle is moving right (up) when

v(t) > 0

A particle is moving left (down) when

v(t) < 0

A particle changes direction when

v(t) changes sign

A particle’s velocity is increasing when

a(t) > 0

A particle’s velocity is decreasing when

a(t) < 0

A particle’s speed is increasing (aka speeding up) when

v(t) and a(t) signs are the same

a particle’s speed is decreasing (aka slowing down) when

v(t) and a(t) signs are different

area of square

A = s²

Area of circle

A = πr²

Volume of circle

A = πr²h

Area of triangle

A = 1/2 bh

Volume of triangle

A = 1/3 Bh

derivative of sec

sec(x)tan(x).

derivative of cot

-csc^2(x)

derivative of csc

-csc(x)cot(x)