Q 11-02-137JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\dfrac32 x$ distance. The average velocity in this motion is $\dfrac{50}{7}\ \text{m/s}$. If $v_1$ is $5\ \text{m/s}$ then $v_2$ = ______ m/s.
Numerical value type. Enter your answer.
Answer: 10
$$v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} = \frac{x + \frac32x}{\frac{x}{5} + \frac{3x}{2v_2}} = \frac{5/2}{\frac15 + \frac{3}{2v_2}}$$
$$\frac{5/2}{\frac15 + \frac{3}{2v_2}} = \frac{50}{7} \Rightarrow \frac15 + \frac{3}{2v_2} = \frac{7}{20} \Rightarrow \frac{3}{2v_2} = \frac{3}{20} \Rightarrow v_2 = 10\ \text{m/s}$$
Solution by Sreeraj P, M.Sc Physics