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A car is moving along a straight road with a uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance with velocity $30\; km / h$ and $40\; km / h$ respectively. The velocity of the car midway between $P$ and $Q$
$33.3 \;km / h$
$25 \sqrt{2} \;km / h$
$20 \sqrt{2}\; km / h$
$35\; km / h$
Solution
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
$V_{\text {mid }}=\sqrt{\frac{V_{p}^{2}+V_{Q}^{2}}{2}}$
$V_{m i d}=\sqrt{\frac{30^{2}+40^{2}}{2}}$
$V_{mid} =\sqrt{\frac{900+1600}{{2}}}$
$V_{{mid}}=\sqrt{\frac{2500}{2}}$
$V_{{mid }} =25 \sqrt{2} m / s$
