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The given velocity-position graph depicts that the motion of the particle is SHM. In SHM, at t = 0, v = 0 and x = x_max. So, option (a) is correct.

1. y = 3 sin(π/2 (50t - x))
2. Wave velocity v = ω/k = 25π/π/2 = 50 m/sec.
3. The velocity of particle v_p = ∂y/∂t = 75π cos(25πt - π/2 x)
4. v_p max = 75π

Correct answer: v_p max = 75π

Solution

The maximum velocity of a particle in SHM is given by v_p max = Aω, where A is the amplitude and ω is the angular frequency. Here, v_p max = 75π matches the given data.

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