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Q.

A car moving along straight line covers 1/5th of total distance with speed v₁ and remaining part of distance with speed v₂. The average speed of carover entire distance is.

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a

$\frac{5 v_{1} v_{2}}{4 v_{2} + v_{1}}$

b

$\frac{4 v_{1} v_{2}}{4 v_{1} + v_{2}}$

c

$\frac{4 v_{1} v_{2}}{5 v_{1} + v_{2}}$

d

$\frac{5 v_{1} v_{2}}{v_{2} + 4 v_{1}}$

answer is A.

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Detailed Solution

Let total distance be ‘s’

$\begin{array}{l} ∴ Average speed = \frac{total distance}{total time} \\ V_{sw} = \frac{s}{t_{1} + t_{2}} \\ ∴ t_{l} = \frac{s}{5 v_{l}}, t_{2} = \frac{4 s}{5 v_{2}} \\ ∴ V_{av} = \frac{s}{\frac{s}{5 v_{l}} + \frac{4 s}{5 v_{2}}} = \frac{s \times 5 v_{l} v_{2}}{{sv}_{2} + 4 {sv}_{l}} \\ ∴ V_{ax} = \frac{s \times 5 v_{1} v_{2}}{s (v_{2} + 4 v_{1})} \\ ∴ V_{sw} = \frac{5 v_{1} v_{2}}{v_{2} + 4 v_{1}} \end{array}$

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A car moving along straight line covers 1/5th of total distance with speed v1 and remaining part of distance with speed v2. The average speed of carover entire distance is.