$ a)\; 4 m/s \\ b)\; 2 m/s \\ c)\; 3 \sqrt 2 m/s \\ d)\; 100/3 m/s $

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Area under the curve $OABC$

$\quad= \large\frac{1}{2} $$ \times (2+4) \times 10 =30$-----(1)

Also area under the $P-x$ graph

$\quad=\int P dx$

$\quad=\large\int $$\bigg(m \large\frac{dv}{dx}\bigg)$$v dx$

$\quad=\int m \;dv\;v \large\frac{dx}{dt} \qquad [\frac{dx}{dt}$$=v]$

$\quad=\int \limits_1^v m\;v^2\;dv$

$\quad=\large\frac{mv^2}{3} \bigg]_1^v$

$\quad= \large\frac{10}{7 \times 3} $$[v^3-1]$----(2)

From (1) and (2)

$\large\frac{10 }{7 \times 3}$$[v^3-1]=30=>v^3-1=63$

$=>v^3=64$

$=>v=4 m/s$

Hence a is the correct answer.

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