Motion In A Straight Line Ques 49
49. A car moves a distance of $200 $ $m$. It covers the first half of the distance at speed $40$ $ km / h$ and the second half of distance at speed $v$. The average speed is $48$ $ km / h$. Find the value of $v$
[1991]
(a) $56$ $ km / h$
(b) $60$ $ km / h$
(c) $50$ $ km / h$
(d) $48$ $ km / h$
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Answer:
Correct Answer: 49.(b)
Solution:
- (b) Given, Total distance $=200$ $ m$
speed in first half distance $=40$ $ km / hr$
speed in second half distance $=v$ $ km / hr$.
$ \begin{aligned} & \text{ So, } v _{a v}=\frac{\text{ Total distance covered }}{\text{ Total time elapsed }} \\ & 48=\frac{200 \times 10^{-3}}{(\frac{100 \times 10^{-3}}{40})+(\frac{100 \times 10^{-3}}{v})} \end{aligned} $
or $\quad \frac{1}{40}+\frac{1}{v}=\frac{2}{48}=\frac{1}{24}$
or $\quad \frac{1}{v}=\frac{1}{24}-\frac{1}{40}=\frac{2}{120}=\frac{1}{60}$
or $\quad v=60 $ $km / h$
BETA
