Question

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 $t=0$)

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

Answer 1

The correct option is B $\frac{b^2\tau }{2}$

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