Streaklines are traced out by neutrally buoyant marker fluid injected into a flow field from a fixed point in space. A particle of the marker fluid that is at a point (x, y) at time t must have passed through the injection point (xo, yo) at some earlier instant t = τ . The initial history of a marker particle may be found by solving the pathline equations for the initial conditions that x = xo, y = yo when t = τ. The present locations of particles on the streakline are obtained by setting equal τ to values in the range 0 <= τ <= t. Consider the flow field V = ax (1 +bt) i^ + cyj^, where a = c = 1s^-1 and b = 0.2 s^-1. Coordinates are measured in meters.
1. Plot the streakline that passes through the initial point (xo. yo) = (1,1), during the interval from t = 0 to t = 3s.