The amplitude of wave disturbance propagating in positive direction of $X$-axis is given by $y=\frac{1}{1+x^{2}}$ at $t=0$ and by $y=\frac{1}{1+(x-1)^{2}}$ at $t=2 \mathrm{~s}$
where $x$ and $y$ are in metres. The shape of the wave disturbance does not change during propagation. The velocity of the wave is.
(a) $0.5 \mathrm{~ms}^{-1}$
(b) $2.0 \mathrm{~ms}^{-1}$
(c) $1.0 \mathrm{~ms}^{-1}$
(d) $4.0 \mathrm{~ms}^{-1}$