A particle is moving with speed $v=v \sqrt{x}$ along positive $x$-axis. Calculate the speed of the particle at time $\mathrm{t}=\mathrm{t}$ (assume that the particle is at origin at $\mathrm{t}=0$).

(C) $\frac{\mathrm{b}^{2} \tau}{\sqrt{2}}$

(D) $\frac{\mathrm{b}^{2} \tau}{4}$

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Kinematics

A particle is moving with speed

v = v x

along positive

x

-axis. Calculate the speed of the particle at time

t = t

(assume that the particle is at origin at

t = 0

(A) $b^{2} τ$
(B) $\frac{b ^{2} τ}{2}$ ✓ Correct
(C) $\frac{b ^{2} τ}{2}$
(D) $\frac{b ^{2} τ}{4}$

Answer: (B)

Solution

Here

v = b x

, so

\frac{d x}{d t} = b x

. Separating the variables,

\frac{d x}{x} = b d t

, and integrating with

x = 0

t = 0

gives

2 x = b t

, so

x = \frac{b t}{2}

. The speed at time

τ

is then

v = b x = b \cdot \frac{b τ}{2} = \frac{b ^{2} τ}{2}

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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