Today, we are going to talk about constant-acceleration motion. 

This will mainly be some mathematics.

Derivation of Equations

Equation of displacement s

Starting with the equation for velocity:

We can solve for time (t) in terms of initial velocity (u), acceleration (a), and final velocity (v):

Now, substitute this value of time into the equation for displacement:

Equation for Final Velocity v

Using the equation for time:

Substitute this value of time into the equation for final velocity:

As you can see, the equation simplifies to just v = v, which is true and consistent.

Equation for Displacement (x) — Alternative Form

Starting with the equation for average velocity:

Rearrange the equation to solve for final velocity:

Substitute this value of final velocity into the equation for displacement:

This derivation confirms the validity of the alternative form of the displacement equation.

Oh my god, that was a lot! Next episode we'll be doing some Calculus... check out our Calculus Articles if you are not familiar with them. 

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