A particle in an experimental apparatus has a velocity given by v = k√s, where v is in millimeters per second, the position s is millimeters, and the constant k = 0.2 mm^1/2s⁻¹. If the particle has a velocity v₀ = 3 mm/s at t = 0, determine the particle position, velocity, and acceleration as functions of time, and compute the time, position, and acceleration of the particle when the velocity reaches 15 mm/s.