Derive the equation (a) s=ut+½at² (b)2as=v²-u²
Answers
Answer:
Explanation:
Consider an object which has travelled displacement s in the time t under uniform acceleration a.Let intial velocity of the object be u and the final velocity v.
s=1/2t(u+v) -1
from the veocity relation
v=u+at -2
substitute 1 in 2
s=1/2t(u+u+at)
=1/2t(2u+at)
s=ut+1/2at^2
b) 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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Answer:
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