The original videos made by Salman Khan are wonderful. The subsequent corrections, additions, and reorganizations made by minions are awful. As of June 2022 there are several different overlapping course outlines, including:

• Middle School Physics - NGSS
• High School Physics
• High School Physics - NGSS
• AP/College Physics 1

We chose the one labelled “Physics Library” https://www.khanacademy.org/science/physics/

Biology
Chemistry
Physics
Math

Math is a pure mental world. Physics applies mathematical models to interactions among objects in the world. Chemistry applies physics models to the smallest elements. Biology is based on chemistry.

\begin{align} \vec{F} &= m \vec{a} && \text{force} = \text{mass times acceleration} \\ \vec{d} &= \vec{v} t && \text{displacement} = \text{velocity times time} \\ \vec{a} &= \frac{\Delta\vec{v}}{\Delta t} && \text{acceleration} = \text{change in velocity over change in time}\\ \end{align}

Isaac Newton - classical mechanics
Max Planck - the very small
Albert Einstein - the very fast, the speed of light

“When you change the way you look at things, the things you look at change.” - Max Planck

\begin{align} s &= d / t && \text{speed = distance / time}\\ s &= 5m / 2s && \text{move a brick 5 meters in 2 seconds}\\ s &= 2.5 m/s && \text{speed is 2.5 meters per second}\\ \\ \vec{v} &= \vec{d} / t && \text{velocity = displacement / time}\\ \vec{v} &= 5m / 2s && \text{move a brick 6 meters to the right in 2 seconds}\\ \vec{v} &= 2.5 m/s \text{ to the right}\\ \end{align}

Point of view from which we measure things.

* ground, stationary * plane, moving to the right at 250 m/s * car, moving to the left at 50 m/s

\begin{align} |\vec{v}| &= s && \text{magnitude of a vector is the speed} \\ |\vec{d}| &= d && \text{magnitude of a displacement is the distance} \\ \end{align}

Using calculus we see that the area under a velocity-time line is distance.

Slope.

Instantaneous vs average velocity.

\begin{align} \vec{a} &= \frac{\Delta v}{\Delta t} && \text{Acceleration = change in velocity over change in time}\\ \vec{a} &= \frac{60 - 0}{3 - 0} && \text{porsche 911 accelerates from 0 to 60 in 3 seconds}\\ \vec{a} &= 20 m/h/s && \text{miles per hour per second}\\ \vec{a} &= \frac{1}{180} m/s^2 && \text{miles per second squared}\\ \end{align}

Displacement per second per second

Acceleration-time line
Rise over run
The area under the line gives the change in velocity

\begin{align} \Delta x &= \text{change in position}\\ t &= \text{time interval}\\ \vec{v}_i &= \text{initial velocity as m/s}\\ \vec{v}_f &= \text{final velocity as m/s}\\ \vec{a} &= \text{constant acceleration in } m/s^2\\ \\ v_f &= v_i + at\\ \Delta x &= v_i t * 1/2 at^2\\ \Delta x &= \frac{v_f + v_i}{2} t\\ v_f^2 &= v_i^2 + 2a\Delta x\\ \end{align}

Projectile motion