The correct option is D At t=0.5 sec, velocity of particle is 0 m/s
The displacement equation for the wave is,
y=10sin(πt+0.5x)
Differentiating above equation partially w.r.t time gives velocity of particle at a fixed position.
⇒vP=∂y∂t
⇒vP=π×10cos(πt+0.5x)
Substituting x=0 in above equation to get particle velocity at x=0,
⇒vP=π×10cos(πt+0)
⇒vP=10πcosπt
At t=0 sec, particle velocity is
vP=10π×cos0∘=10π m/s
At t=3 sec
vP=10πcos(3π)=−10π m/s
similarly, at t=0.5 sec
vP=10πcos(π/2)=0 m/s