Displacement & Velocity Study Notes

Motion can be described using words, mathematical equations, or graphs showing changes over time.
Reference Point: A stationary place or object (such as a tree or building) used for comparison to determine if an object is in motion.
Motion is relative and depends entirely on the chosen point of reference.

Scalar Quantities: Physical quantities that have magnitude (size) only, with no direction.
- Examples: Distance, Speed, Mass, Energy, Density, Power, Length, Area, Volume, Time, Temperature, Work.
Vector Quantities: Physical quantities that have both magnitude and direction.
- Examples: Displacement, Velocity, Weight, Acceleration, Force, Impulse, Pressure, Momentum, Gravity, Drag.

Position: The separation between an object and a reference point; a vector quantity containing magnitude and direction.
Distance ( $d$ ): The total length measured between two points without reference to direction; a scalar quantity measured in meters ( $\text{m}$ ) or kilometers ( $\text{km}$ ).
Displacement ( $\Delta \vec{d}$ ): The change in position or shortest straight-line distance between two points; a vector quantity measured in meters ( $\text{m}$ ) or kilometers ( $\text{km}$ ).
- Equation: $\Delta \vec{d} = \vec{d}_{\text{final}} - \vec{d}_{\text{initial}}$
- Can be positive or negative depending on direction.

Speed ( $v$ ): A scalar rate of motion measuring distance traveled per unit time ( $\text{speed} = \frac{\text{distance}}{\text{time}}$ ). Always positive.
- Average Speed Equation: $\text{avg. speed} = \frac{\text{total distance}}{\text{total time}}$
Velocity ( $\vec{v}$ ): A vector quantity representing speed in a given direction ( $\text{velocity} = \frac{\text{displacement}}{\text{time}}$ ).
Average Velocity ( $\vec{v}_{\text{AVE}}$ ): The ratio of net displacement to elapsed time: $\vec{v}_{\text{AVE}} = \frac{\Delta \vec{d}}{\Delta t} = \frac{\vec{d}_2 - \vec{d}_1}{t_2 - t_1}$
Constant / Uniform Velocity: Motion where the average velocity remains identical across all time intervals ( $\vec{v} = \frac{\vec{d}}{t}$ ).

Formula Rearrangements:
- Displacement: $\Delta \vec{d} = \vec{v} \times t$
- Velocity: $\vec{v} = \frac{\Delta \vec{d}}{\Delta t} = \frac{\vec{d}_2 - \vec{d}_1}{t_2 - t_1}$
- Time: $t = \frac{\Delta \vec{d}}{\vec{v}}$
Speed and Velocity Unit Conversions:
- To convert from $\text{km/h}$ to $\text{m/s}$ : divide by $3.6$
- To convert from $\text{m/s}$ to $\text{km/h}$ : multiply by $3.6$