Derive equation v^{2}-u^{2}=2 a S graphically.

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7. MOTION

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Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

Option A

Option B

Option C

Option D

Solution

Consider the figure given below

Now, area of trapezium $OABD$

$=\frac{( OA + BD ) \times OD }{2}$

Now, $OA =u, BD =v,$ and $OD =t$

Therefore, we have

$S =\frac{(u+v) t}{2}$

or $S=\frac{(u+v)(v-u)}{2 a},$ using $v=u+a t$

Hence, we have

$v^{2}-u^{2}=2 a S$

Standard 9

Science

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