Given that S = \(3t^{2}\) + 5t - 10 is displacement of a particle in metres,...

Given that S = \(3t^{2}\) + 5t - 10 is displacement of a particle in metres, calculate it initial velocity.

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.

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