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Question

A car covers the first half of the distance between two places at $$40kmph$$ and the other half at $$60kmph$$. The average speed of the car is :


A
40kmph
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B
48kmph
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C
50kmph
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D
60kmph
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Solution

The correct option is B $$48kmph$$
Given,

$$v_1=40kmph$$

$$v_2=60kmph$$

Lets consider $$d=$$ total distance 

The time taken to compete half distance with speed $$v_1$$,

$$t_1=\dfrac{d}{2v_1}$$

The time take to complete second half distance with speed $$v_2$$

$$t_2=\dfrac{d}{2v_2}$$

Total time, $$t=t_1+t_2$$

$$t=\dfrac{d}{2v_1}+\dfrac{d}{2v_2}$$

$$t=\dfrac{d}{2}(\dfrac{1}{v_1}+\dfrac{1}{v_2})=\dfrac{d(v_1+v_2)}{2v_1v_2}$$. . . . . . . . .(1)

The average speed of the car is given,

$$v_{avg}=\dfrac{d}{t}$$

$$v_{avg}=\dfrac{2v_1v_2}{v_1+v_2}$$   (from equation 1)

$$v_{avg}=\dfrac{2\times 40\times 60}{40+60}=48kmph$$

The correct option is B.

Physics

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