third law of motion. 2as= v²-u² MathmaticalProof
Answers
The total distance travelled, S = Area of trapezium OABC.
So, S= 1/2(SumofParallelSides)×Height
S=(OA+CB)×OC
Since, OA = u, CB = v, and OC = t
The above equation becomes
S= 1/2(u+v)×t
Now, since t = (v – u)/ a
The above equation can be written as:
S= 1/2(u+v)×(v-u)/a
Rearranging the equation, we get
S= 1/2(v+u)×(v-u)/a
S = (v²-u²)/2a
Third equation of motion is obtained by solving the above equation:
v² = u²+2aS
=> 2aS=v²-u²
Step-by-step 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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