A body traversed half of the distance with a velocity $V_0$. The remaining part $V_1$ for half of the time and with the velocity $V_2$ for the other half of the time. Find the average velocity of the body over the whole journey.
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$\dfrac{2V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
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$\dfrac{3V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
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$\dfrac{2V_0(V_1 + V_2)}{(3V_0 + V_1 + V_2)}$
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$\dfrac{V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
A
Correct answer
Explanation
Let total distance be 2d. Time for first half is d/V0. For the second half, time is t. Distance covered is (V1*t/2) + (V2*t/2) = d. So t = 2d/(V1+V2). Total time = d/V0 + 2d/(V1+V2) = d(V1+V2+2V0)/(V0(V1+V2)). Average velocity = 2d / total time = 2V0(V1+V2)/(2V0+V1+V2).