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

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Kinematics

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

Answer: 50

Solution

Let the whole path be

2 x

. The first half

x

is ridden at

5 m/s

in time

\frac{x}{5}

. In the second half the two equal time intervals at

10 m/s

and

15 m/s

cover

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

, so that stretch takes

t = \frac{2 x}{25}

. The total time is

\frac{x}{5} + \frac{2 x}{25} = \frac{7 x}{25}

, and the mean speed is

\frac{2 x}{7 x /25} = \frac{50}{7} m/s

. Hence

x = 50

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Integer answer

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