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  • A vehicle travels half the distance L with speed V_{1} and the other half with speed V_{2}, then its average speed is

A vehicle travels half the distance L with speed V_{1} and the other half with speed V_{2}, then its average speed is

a) \frac{(V_{1}+V_{2})}{2}

b) \frac{(2V_{1}+V_{2})}{(V_{1}+V_{2})}

c) \frac{(2V_{1}V_{2})}{(V_{1}+V_{2})}

d) \frac{L(V_{1}+V_{2})}{V_{1}V_{2}}

Answers (1)

The correct answer is the option c) \frac{(2V_{1}V_{2})}{(V_{1}+V_{2})}

Explanation: Let t_{1} be the time taken in half distance, t_{1}=\frac{L}{v_{1}}

Let t_{2} be the time taken in half distance, t_{2}=\frac{L}{v_{2}}

Therefore, the total time taken in distance will be equal to (L+L)=\frac{L}{v_{1}}+\frac{L}{v_{2}}

                                                                                                               =\frac{L(v_{1}+v_{2})}{v_{1}v_{2}}

& the total distance will be equal to L + L = 2L

Thus, the average speed will be,

v_{av}=\frac{Total \; distance}{Total\; time}

        \\=\frac{2L}{\frac{L(v_{1}+v_{2})}{v_{1}v_{2}}}\\\\=\frac{2V_1V_2}{V_1+V_2}

Posted by

infoexpert22

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