Assume acceleration of the car is a.

$PQ = s$

Using, $v^{2}=u^{2}+2$ as.

$\Rightarrow 40^{2}=30^{2}+2 a s$

$\Rightarrow 2$ as $=700\Rightarrow$ as $=350$

Now, assume velocity of car at a midpoint of $PQ$ is $V$. $V ^{2}= vp ^{2}+2 a \left(\frac{ s }{2}\right)$

$\Rightarrow V^{2}=900+350=1250$

$\Rightarrow V =35.35\;{ m }/{ s }$

OR

$V_{\text {mid }}=\sqrt{\frac{V_{p}^{2}+V_{Q}^{2}}{2}}$

$V_{m i d}=\sqrt{\frac{30^{2}+40^{2}}{2}}$

$V_{mid} =\sqrt{\frac{900+1600}{{2}}}$

$V_{{mid}}=\sqrt{\frac{2500}{2}}$

$V_{{mid }} =25 \sqrt{2} m / s$