Speed and Velocity

Average Speed Formula

Speed = Total Distance / Total Time

Average Velocity Formula

Velocity = Total Displacement / Total Time

1D Displacement Formula

Displacement = Final Position - Initial Position (x_f - x_i)

2D Displacement Formula

Displacement = √(a² + b²) [Pythagorean Theorem]

Density Formula

Density (ρ) = Mass / Volume

Volume from Density Formula

Volume = Mass / Density

Water Displacement Formula

Volume = Final Water Level - Initial Water Level

Minutes to Hours Conversion

Divide total minutes by 60 (e.g., 30 min = 30/60 = 0.5 hours)

Scalar Quantity

A measurement that has magnitude (amount) only, with no direction (e.g., speed, distance, mass).

Vector Quantity

A measurement that has both magnitude (amount) AND direction (e.g., velocity, displacement).

Distance

The total length of the path traveled; always positive and scalar.

Displacement (Δx)

The straight-line distance and direction from start to end; vector quantity.

Speed

How fast an object moves (Distance / Time); scalar quantity.

Velocity

How fast and in what direction an object moves (Displacement / Time); vector quantity.

Round Trip Rule

If an object starts and ends at the exact same location, its total displacement is 0, so its average velocity is 0.

Density (ρ)

The amount of mass per unit volume of a substance.

Mass (m)

The amount of matter in an object (measured in g or kg).

Volume (V)

The amount of 3D space an object occupies (measured in mL, cm³, or L).