A horse rider covers half the distance with 5 m/s speed. The remaining part of the distance was travelled with speed 10 m/s for half the time and with speed 15 m/s for the other half of the time. The mean speed of the rider averaged over the whole time of

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Solution

Q.
A horse rider covers half the distance with 5 m/s speed. The remaining part of the distance was travelled with speed 10 m/s for half the time and with speed 15 m/s for the other half of the time. The mean speed of the rider averaged over the whole time of motion is $x / 7$ m/s. The value of $x$ is ______. [2023]

Ans.
(50)

$t_{A B} = \frac{x}{5 m/s}$

In motion BC, $x = d_{1} + d_{2}$

where $d_{1}$ and $d_{2}$ are the distances travelled with 10 m/s and 15 m/s respectively in equal time intervals $\frac{' t'}{2}$ each.

$d_{1} = \frac{10 t}{2}, d_{2} = \frac{15 t}{2}$

$d_{1} + d_{2} = x = \frac{t}{2} (10 + 15) = \frac{25 t}{2}$

$< v > = \frac{2 x}{\frac{x}{5} + \frac{2 x}{25}} = \frac{2 \times 25}{5 + 2} = \frac{50}{7} m/s$

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