The initial velocity (v) is obtained by differentiating the displacement (S) with respect to time, which gives: v = \(\frac{dS}{dt}\) = \(\frac{d}{dt}\)(\(3t^2\) + 5t - 10) = 6t + 5 The initial velocity is the velocity of the particle at time t = 0. Substituting t = 0 into the velocity equation: v(0) = 6(0) + 5 = 5 Therefore, the initial velocity of the particle is 5 m/s.