Question

v^2-u^2=2as prove it​

Answer 1

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+

2

1

at

2

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=

a

v−u

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

S=ut+

2

1

at

2

becomes,

S=u(

a

v−u

)+

2

1

a(

a

v−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

Answer 2

Answer:

First of all you have to know the other two equations of motions :

V=u+at

S=ut+1\2at2

Now the derivation:

From the first equation we have :

at=v−u

t=v−u\a

Now putting the value of t in the second equation of motion:

s=u(v−u\a)+1\2a(v−u\a)2

s=uv−u2\a+a(v2+u2–2vu)\2a2

s=uv−u2\a+(v2+u2+2vu)\2a

s=(2uv−2u2+v2+u2–2vu)\2a

2as=v2−u2

v2=u2+2as

So here it is.. hope it helps :)

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