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