Question

prove that;
v=u+at
v2=u2+2as

Answer 1

Answer:

Explanation:

We know acceleration (a) = rate of change of velocity

                                         

                                           = changeinvelocity  

                                              time period

                                           =   finalvelocity−initialvelocity

                                                      timeperiod

​                                      =v−u

                                               t

                                         ∴a=  v−u

                                               t

ora×t=v−u

or at = v - u or at + u = v

∴ v = u + at

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+1/2at²  and v=u+at, include the time variant t

There 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=  v−u

     a

and use this to replace t wherever it appears in the second equation. So

S=ut+1/2at²   becomes,

S=u(v−u ) + 1/2  a (v-u)²

          a                       t

⇒2aS=2u(v−u)+(v−u) ²

⇒2aS=2uv−2u²  −v  ²−2uv−u²  

⇒2aS=v ²-u²

⇒v²= u²   +2aS

hope this helps u