Analyze a problem situation that can be represented algebraically by a polynomial function such as the following: 3 1) A particle moves along the x-axis so that its position at time t is given by the function. x(t) == t - 3t +5t+3 for t 0. The velocity of the particle at time t is given by v(t) = 2 - 6t+5, for t 0. a) Where is the particle at time t = 0? b) At what time(s) is the particle at the origin? c) When is the particle to the left of the origin? d) Where is the particle when it stops? e) When is the particle moving to the left? f) In which direction is the particle moving as t ? Explain.