Kinematic Formulae

Note: The images use "x" for displacement, meanwhile I use "s" in the flashcards and notes.

State the equation for final velocity.

v = u + at.

Derive the equation v = u + at.

This equation can be derived from the definition of acceleration (a = (v - u)/t) rearranged to solve for final velocity (v) as v = u + at.

State the equation for displacement

s = ut + 1/2at²

Derive the equation for displacement

Displacement is equal to Average Velocity over Time, written as (v-u)/2*t

v can be rewritten as u + at

Multiplying the numerator by t and dividing it all by 2 will give you ut + 1/2at²

State the equation you can use if you don’t have t (v² formula)

v² = u² + 2as

Derive the v² formula

v² = (u + at)(u + at) = u² + 2uat + a²t²

Take away 2a from the second half of the formula, giving you u² + 2a(ut + 1/2at²)

Look familiar? What’s inside the bracket is the formula for displacement! That entire bracket can be rewritten as “s”

Therefore v² = u² + 2as