SATHEE: Motion in a Straight Line

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 $40 k m / h$ and the second half of distance at speed $v$ . The average speed is $48 k m / h$ . Find the value of $v$

(a) $56 k m / h$

(b) $60 k m / h$

(d) $48 k m / h$

[1991]

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Answer:

Correct Answer: 7. (b)

Solution:

(b) Given, Total distance $= 200 m$ speed in first half distance $= 40 k m / h r$ speed in second half distance $= v k m / h r$ .

$\begin{aligned} So, v_{a v} = \frac{Total distance covered}{Total time elapsed} \\ 48 = \frac{200 \times 10^{- 3}}{(\frac{100 \times 10^{- 3}}{40}) + (\frac{100 \times 10^{- 3}}{v})} \end{aligned}$

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 $v = 60 k m / h$

$\Rightarrow v = 60 k m / h$

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Motion in a Straight Line - Result Question 7

7. A car moves a distance of 200m. It covers the first half of the distance at speed 40km/h and the second half of distance at speed v. The average speed is 48km/h. Find the value of v

Answer:

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7. A car moves a distance of $200 m$ . It covers the first half of the distance at speed $40 k m / h$ and the second half of distance at speed $v$ . The average speed is $48 k m / h$ . Find the value of $v$