Q 11-02-074JEE MainJEE Main 2023 (30 Jan, Shift 1)Medium
A horse rider covers half the distance with $5\ \text{m s}^{-1}$ speed. The remaining part of the distance was travelled with speed $10\ \text{m s}^{-1}$ for half the time and with speed $15\ \text{m s}^{-1}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\dfrac{x}{7}\ \text{m s}^{-1}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 50
Let the total distance be $2d$. First half takes $\dfrac d5$.
In the second half equal times at 10 and 15 give an average $12.5\ \text{m s}^{-1}$, so it takes $\dfrac{d}{12.5}$.
$$\bar v=\frac{2d}{\frac d5+\frac d{12.5}}=\frac{2}{0.2+0.08}=\frac{2}{0.28}=\frac{50}{7}\ \text{m s}^{-1}$$
So $x=50$.
Solution by Sreeraj P, M.Sc Physics