### Linear Motion  --- ### How far? **Distance** is the measurement of how far you're traveled. Treasure Hunt lab: Total distance traveled from A to B to C to D etc... It's a scalar! --- ### How far and what direction? **Displacement** is the measurement of change in position and what direction. Treasure Hunt lab: Final pos minus initial position, compass direction. It's a vector! --- ### How fast? **Speed** is a measurement of how fast something is moving. Change in distance over time: `$$ s = \frac{d} {t} $$` It's a scalar! --- ### How fast and what direction? **Velocity** is a measurement of how fast something is moving in a direction. Change in displacement over time: `$$ \Delta \vec v = \frac{\Delta \vec x} {\Delta t} $$` `$$ \Delta \vec x = x_f - x_i $$` (x final minus x initial) It's a vector! Units: `$$ \frac{m} {s} $$` --- A change is represented with the Greek capital delta `$$ \Delta $$` --- ### Instantaneous velocity `$$ v = at $$` Where `a` is acceleration. --- ### Acceleration is a change in velocity `$$ \Delta \vec a = \frac{\Delta \vec v} {\Delta t} $$` Units: `$$ \frac{m} {s^2} $$` --- ### Most of the time... We'll simplify the notation of the equations. `$$ v = \frac{x} {t} $$` `$$ a = \frac{v} {t} $$` --- ### Acceleration due to gravity `$$ g = 9.81 \frac{m} {s^2} $$` Sometimes we round to 9.8 or even 10. --- ### Free fall equation In this equation, `y` is the vertical displacement fallen. `$$ y = \frac{1} {2} gt^2 $$` --- ### Free fall equation solve for time `$$ t = \sqrt \frac{2y} {g} $$` --- ### Example problem: A guy named Grapenuts falls 235 meters off a cliff in the Grand Canyon. How long (in seconds) until splat?