Question

Derive the formula of v^2-u^2=2as​

Answer 1

Explanation:

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

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