Question

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

• A. $\frac{b^2 \tau}{4}$
• B. $\frac{b^2 \tau}{2}$
• C. $b^2 \tau$
• D. $\frac {b^2 \tau}{1}$
• E. $\frac{b^2 \tau}{\sqrt{2}}$

Answer 1

Answer: (B)

$v = b\sqrt{x}$
$\frac{dv}{dt} = \frac{b}{2\sqrt{x}} \frac{dx}{dt}$
$a = \frac{bv}{2\sqrt{x}}$
$a = \frac{b(b\sqrt{x})}{2\sqrt{x}}$
$\frac{dv}{dt} = a = \frac{b^2}{2}$
$ \, \, \, v = \frac{b^2}{2} \tau$