Motion In A Straight Line Ques 28
28. 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 $Q$ is
[1988]
(a) $33.3$ $ km / h$
(b) $20 \sqrt{2} $ $km / h$
(c) $25 \sqrt{2}$ $ km / h$
(d) $35$ $ km / h$
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Answer:
Correct Answer: 28.(c)
Solution:
- (c) Let $PQ=x$, then
$u=30$ $km / h$
$v=40 $ $km / h$
$a=\frac{40^{2}-30^{2}}{2 x}=\frac{350}{x} \quad [\because v^{2}=u^{2}+2 a s]$
Also, velocity at mid point is given by $v_m$,
$\Rightarrow v_m=u^{2}+20(7)$
$\Rightarrow v_m^{2}-30^{2}=2 \times \frac{350}{x} \times \frac{x}{2}$
This gives $v=25 \sqrt{2} $ $km / h$
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