# 4.04 Equations of motion

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 = (v2 + u2)/2a
Therefore 2as = v2 + u2
rearranging further gives

v2 = u2 +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)]

## Units of measurement

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!

• Displacement "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)