Question

v^2=u^2+2as proof by calculus

Answer 1

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Answer 2

Answer:

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+ 1/2 at²

andv=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 .appears in the second equation. So.

s=ut+1/2 at² becomes,

s= u(.v-u/a)+1/2 a(.v-u/a)²

⇒2aS=2u(v−u)+(v−u) ²

2aS=2uv−2u² −v ²−2uv−u ²

⇒2aS=2uv−2u ² −v ²−2uv−u²

2aS=v ²−u ²

.v²=u²+2as