The last equation is derived from equations (1) and (2)

**Equation 4**

Equation 1 states that; s = (v + u)/2 x t

Equation 2 states that; v = u + at therefore (v - u)/a = t

Using equation 2 to substitute for t in equation 1 gives

s = (v + u)/2 x (v - u)/a

s = (v^{2} + u^{2})/2a

Therefore 2as = v^{2} + u^{2}

rearranging further gives

** v ^{2} = u^{2} +2as (eq. 4)**

[This gives a useful equation for an object moving with constant acceleration which does not require information about time ( i.e. there is no "t" in this equation)]

In this section we have derived four equations for the motion of an object travelling with constant acceleration. In order to use these equations to
calculate values we **must** enter the correct units of measurement!

- Di
**s**placement "s" is measured in metres (m) - Time "t" is measured in seconds (s)
- Velocity "u" or "v" is measured in metres per second (ms
^{-1}) - Acceleration "a" is measured in metres per second per second (ms
^{-2})