Final answer:
The momentum of a 3 kg particle as a function of time with given velocity is (6i + 9tj) kg*m/s. The net force acting on the particle is (0i + 9j) N, corresponding to the time-invariant j-component of acceleration.
Step-by-step explanation:
The momentum p(t) of a particle as a function of time is given by the formula p(t) = m * v(t), where m is the mass and v(t) is the velocity of the particle at time t. For a 3 kg particle with a velocity v(t) = (2i + 3tj) m/s, the momentum function is p(t) = 3 kg * (2i + 3tj) m/s = (6i + 9tj) kg*m/s.
The net force acting on this particle can be inferred from the second derivative of the position function, in this case, the derivative of the velocity function, v'(t). Since the i component of velocity is constant and the j component is linearly increasing with time, it suggests that there is no net force in the i direction and a constant net force in the j direction. Therefore, the net force F acting on the particle is given by the mass times the acceleration (0i + 3j) m/s2 so, F = m * a = 3 kg * (0i + 3j) m/s2 = (0i + 9j) N.