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 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 ___________. Numerical answer type. Work it out, then open the answer.

Answer: 50. Second half in equal times at 10 and 15 m/s: its average speed = (10 + 15)/(2) = 12.5 m/s. Now two equal distances at 5 and 12.5 m/s: vavg = (2(5)(12.5))/(5 + 12.5) = (125)/(17.5) = 50/7 m/s So x = 50.

A horse rider covers half the distance with 5 m/s speed. The… | JEE Main 2023 (30 Jan, Shift 1)

Q14JEE Main 2023 · 30 JAN · SHIFT 1Medium

Distance, Displacement & Average Speed

A horse rider covers half the distance with $5\text{ m/s}$ speed. The remaining part of the distance was travelled with speed $10\text{ m/s}$ for half the time and with speed $15\text{ m/s}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7}\text{ m/s}$ . The value of $x$ is ___________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 50

Second half in equal times at 10 and 15 m/s: its average speed $= \frac{10 + 15}{2} = 12.5$ m/s.
Now two equal distances at 5 and 12.5 m/s: $v_{avg} = \frac{2(5)(12.5)}{5 + 12.5} = \frac{125}{17.5} = \frac{50}{7}$ m/s
So $x = 50$ .

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