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

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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