Motion in a Straight Line - Result Question 7
7. 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 $v$
(a) $56 km / h$
(c) $50 km / h$
(b) $60 km / h$
(d) $48 km / h$
[1991]
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Answer:
Correct Answer: 7. (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 $\frac{1}{40}+\frac{1}{v}=\frac{2}{48}=\frac{1}{24}$
or $\frac{1}{v}=\frac{1}{24}-\frac{1}{40}=\frac{2}{120}=\frac{1}{60}$
or $v=60 km / h$
$\Rightarrow v=60 km / h$
