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  • An object moves with speed v1, v2 and v3 along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be: <img alt

An object moves with speed v1, v2 and v3 along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

Option: 1

\frac{\left(v_1+v_2+v_3\right)}{3 v_1 v_2 v_3}


Option: 2

\frac{\left(v_1+v_2+v_3\right)}{_3}


Option: 3

\frac{3 v_1 v_2 v_3}{\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}


Option: 4

\frac{3 v_1 v_2 v_3}{3\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}


Answers (1)

best_answer

 

\begin{aligned} \langle v\rangle & =\frac{\text { Total distance }}{\text { Total time }} \\ & =\frac{3 \mathrm{x}}{\frac{\mathrm{x}}{\mathrm{v}_1}+\frac{\mathrm{x}}{\mathrm{v}_2}+\frac{\mathrm{x}}{\mathrm{v}_3}} \\ & =\frac{3}{\left[\frac{1}{\mathrm{v}_1}+\frac{1}{\mathrm{v}_2}+\frac{1}{\mathrm{v}_3}\right]}=\frac{3}{\left[\frac{\mathrm{v}_2 \mathrm{v}_3+\mathrm{v}_1 \mathrm{v}_3+\mathrm{v}_1 \mathrm{v}_2}{\mathrm{v}_1 \mathrm{v}_2 \mathrm{v}_3}\right]} \\ \langle\mathrm{v}\rangle & =\frac{3 \mathrm{v}_1 \mathrm{v}_2 \mathrm{v}_3}{\left[\mathrm{v}_3 \mathrm{v}_2+\mathrm{v}_1 \mathrm{v}_2+\mathrm{v}_1 \mathrm{v}_2\right]} \end{aligned}

 

Posted by

SANGALDEEP SINGH

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