The correct option is D 0.5 m/s
Given, wave function
y(x,0)=11+x2 ....(i) at t=0
and at t=2 s, y(x,2)=11+(x−1)2 ....(ii)
comparing Eq.(ii) with the equation of travelling wave in format y(x,t)=f(x−vt)
⇒We get that (x−1)=x−vt
putting t=2 s and on equating,
⇒2v=1
⇒v=0.5 m/s
Hence, option (d) is correct.