Question

Derive V²-U² = 2as from fist two equation of motion... Please help no spam ❌ Or moderator will ban account​

Answer 1

Answer:

First of all you have to know the other two

equations of motions :

1. V=u+at

2. 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

:- v2 = u2 + 2asv2=u2+2as

HOPE IT IS HELPFULL TO YOU...

Answer 2

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
+



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