**Density**is the ratio of a substance's mass to its volume and can be expressed mathematically as

whereD=M/V

*D*is density,

*M*is mass, and

*V*is volume.

**Temperature**:

In science, we will use Celsius or Kelvin temperature scales to describe temperature.

To convert:

Celsius = Kelvin - 273.15

Kelvin + 273.15 = Celsius

Kelvin = Celsius + 273.15

Celsius + 273.15 = Kelvin

**Gas Laws:**

*Charles's Law*

The volume of a gas is directly proportional to its temperature in kelvins if the pressure and number of molecules are constant.

V1T1=V2T2

*Boyle's Law*

The volume of a gas is inversely proportional to its pressure if the temperature and the number of molecules are constant.

P1V1=P2T2

*Combined Gas Law*

Pressure is inversely proportional to volume, or higher volume equals lower pressure. Pressure is directly proportional to temperature, or higher temperature equals higher pressure.

(P1V1)/T1=(P2V2)/T2

**Motion**:

wherevf = vi + at

*vf*is final velocity,

*vi*is initial velocity,

*a*is acceleration, and

*t*is elapsed time.

wherev(ave) = (vf+vi)/2

*v(ave)*is average velocity,

*vf*is final velocity, and

*vi*is initial velocity.

df = di + vit + 1/2at^{2}

wheredfis the final, total displacement…

diis the initial displacement. (How far from whatever point of reference is the object when the thing starts accelerating?)…

viis the initial velocity of the object at the beginning of the acceleration.

tis the elapsed time from the beginning of the acceleration until the end of the period being observed.

(vitaccounts for the motion of the object based on its starting velocity. It keeps covering distance at the initial rate, and additionally, it accelerates and covers more distance.)

ais the acceleration andtis elapsed time.

**Force**:

Where

*F*is force,

*a*is acceleration, and

*m*is mass, then:

F = ma

**Work and Energy**:

**Work**is found by

whereW = Fd

*W*is work,

*F*is force applied (not net force!), and

*d*is displacement/distance.

**Kinetic energy**(KE) is found with this equation:

whereKE = 1/2 mv^{2}

*KE*is kinetic energy,

*m*is mass and

*v*is velocity.

The

**potential gravitational energy**can be found with this equation:

wherePE = mgh

*PE*is potential gravitational energy,

*m*is mass,

*g*is acceleration due to gravity, and h is height.

On earth, acceleration due to gravity is 9.8 (m/s)/s

The amount of

**elastic potential energy**is determined by how hard it is to compress or stretch something and how far it is stretched or compressed.

The equation to find this is:

wherePE = 1/2kd^{2}

*PE*is potential elastic energy,

*k*is a constant specific to a particular stretchy thing (spring, rubber band, etc.) and d is the distance that it is stretched or compressed (sometimes x is used instead of

*d*, as in the illustration)

**Heat/Energy Transfer**

Now to find heat, we can use the formula:

WhereQ = mcΔT

*Q*is heat or thermal energy,

*m*is mass,

*c*is a number called specific heat that you either look up or calculate, and

*ΔT*is the change in temperature.