A particle travels half the distance of a straight journey with a speed $5 m / s$ . The remaining part of the distance is covered with speed $6 m / s$ for half the remaining time, with speed $4 m / s$ for the other half of the remaining time. The average speed of the particle is

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$3 m / s$

$4 m / s$

$\frac{3}{4} m / s$

$5 m / s$

answer is D.

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Detailed Solution

From the given question and the figure, we can write

$s = 5 t_{1}, s = 6 t + 4 t = 10 t$

Then we will get

$v_{a v} = \frac{2 s}{t_{1} + 2 t} = \frac{2 s}{\frac{s}{5} + \frac{s}{5}} = \frac{2 s \times 5}{2 s} = 5 m / s$

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