Newton's Equations Relation explained between. 1) v=u+ at 2 1 ? 2) s= ut + Fate 3) v2=u2+2 as ?
Answers
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+ 21 at 2 andv=u+at, include the time variant tThere 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= av−u and use this to replace t wherever it appears in the second equation. SoS=ut+ 21 at 2 becomes,S=u( av−u )+ 21 a( av−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
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:
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