A horse rider covers half the distance with 5 m s - 1 speed. The remaining part of the distance was travelled with speed 10 m s - 1 for half the time and with speed 15 m s - 1 for other half of the ti

Question

A horse rider covers half the distance with 5 m s - 1 speed. The remaining part of the distance was travelled with speed 10 m s - 1 for half the time and with speed 15 m s - 1 for other half of the time. The mean speed of the rider averaged over the whole time of motion is x 7 m s - 1 . The value of x is ______.

TestHub · Accepted Answer

Let total distance travelled by horse rider be $2 x$ .

Now, the time taken to cover first half distance is $t_{A B} = \frac{x}{5}$

Second half distance $x$ between $B C$ is covered in two parts, $x = d_{1} + d_{2}$

here $d_{1}$ is the distance travelled with $10 m s^{- 1}$ and $d_{2}$ is the distance travelled with $15 m s^{- 1}$ in equal time intervals $\frac{t}{2}$ each.

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

Second half distance $x = \frac{t}{2} (10 + 15) = \frac{25 t}{2}$

Now, the mean speed of rider is $v = \frac{2 x}{\frac{x}{5} + \frac{2 x}{25}} = \frac{2 \times 25}{5 + 2} = \frac{50}{7} m s^{- 1}$

Thus, the value of $x = 50$ .

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