We will use both of the EQUATIONS of motion to REACH the third equation of motion. This will require a BIT of algebra.S=ut+ 21 at 2 andv=u+at, include the time variant tThere will be some situations when we do not have any information about time and so it would be a good idea to DERIVE an equation that does not have a t term.To do this, we rearrange our first equation to get t= av−u and use this to replace t wherever it APPEARS in the second equation. SoS=ut+ 21 at 2 becomes,S=u( av−u )+ 21 a( av−u ) 2 ⇒2aS=2u(v−u)+(v−u) 2 ⇒2aS=2uv−2u 2 −v 2 −2uv−u 2 ⇒2aS=v 2 −u 2 ⇒v 2 =u 2 +2aSWe will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.S=ut+ 21 at 2 andv=u+at, include the time variant tThere will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.To do this, we rearrange our first equation to get t= av−u and use this to replace t wherever it appears in the second equation. SoS=ut+ 21 at 2 becomes,S=u( av−u )+ 21 a( av−u ) 2 ⇒2aS=2u(v−u)+(v−u) 2 ⇒2aS=2uv−2u 2 −v 2 −2uv−u 2 ⇒2aS=v 2 −u 2 ⇒v 2 =u 2 +2aS