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Question

A body covers half the distance with a speed of $$20\:m/s$$ and the other half with $$30\:m/s$$. The average speed of the body during the whole journey is


A
Zero
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B
24m/s
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C
25m/s
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D
None of the above
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Solution

The correct option is B $$24\:m/s$$
Given that,
A body covers half the distance with a speed of $$20\ m/s$$ and the other half with $$30\ m/s$$.
Let us considered the total distance is $$2n\ m$$.

A body covers $$n$$ distance with a speed of $$20\ m/s$$

Then, the time is

$$t_{1}=\dfrac{n}{20}$$......(I)

The other $$n$$ distance with a speed $$30\ m/s$$.

Then, the time is

$$t_{2}=\dfrac{n}{30}$$....(II)

 Now, the total time is

$$t=t_{1}+t_{2}$$

$$t=\dfrac{n}{20}+\dfrac{n}{30}$$

$$t=\dfrac{5n}{60}\ s$$

The average speed is

$$\Delta v=\dfrac{2n}{\dfrac{5n}{60}}$$

$$\Delta v=24\ m/s$$

The average velocity is $$24\ m/s$$

Hence, The correct option is B.

Physics

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