Kinematic Formulae

The Kinematic formulae used to define velocity, displacement and acceleration:

• v = u + at

• s = ut + 1/2at²

• v² = u² + 2as (used for when you don’t have t)

v is final velocity

u is initial velocity

s is displacement

a is acceleration

t is time

Deriving the kinematic formulae

Velocity

v = u + at

First, we look at the formula for acceleration. a = v-u/t

By rearranging, we get v = u+at

Displacement

s = ut + 1/2at²

Displacement = Average velocity/time = ((v+u)/2)t

But v = u+at

((u+at+u)/2)t - Multiply the numerator by t

(ut+at²+ut)/2 - Divide by 2

Therefore s = ut + 1/2at²

Time

v² = u² + 2as

v = u + at

So v² is (u + at)(u + at) = u² + 2uat + at² which is also equal to u² + 2a(ut+1/2at²)

However, s = ut + 1/2at²

Therefore v² = u² + 2as

Other Formulae that you can get from these !

Position = Initial Position + Displacement formula

xf = xi + ut + 1/2at²

Initial Velocity = Rearrange the velocity formula

u = v - at

Time (when the object moves from rest) = Rearrange the displacement formula

t = √2x/a