Q 11-02-127JEE MainJEE Main 2019 (12 Apr, Shift 2)Medium
A particle is moving with speed $v = b\sqrt x$ along positive $x$-axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at origin at $t = 0$)
Answer: (C) $\dfrac{b^2\tau}{2}$
$$\frac{dx}{dt} = b\sqrt x \Rightarrow \int_0^x\frac{dx}{\sqrt x} = \int_0^\tau b\,dt \Rightarrow 2\sqrt x = b\tau$$
$$v = b\sqrt x = \frac{b^2\tau}{2}$$
Solution by Sreeraj P, M.Sc Physics