Consider a particle moving along x-axis. Its distance from origin O is described by the co-ordinate x which varies with time. At a time t_(1), the particle is at point P, where its co-ordinate is x_(1) and at time t_(2), the particle is at point Q, where its co-ordinate is x_(2). The displacement during the time interval from t_(1) to t_(2) is the vector from P to Q, the x-component of this vector is (x_(2) - x_(1)) and all other components are zero. It is convenient to represent the quantity x_(2) - x_(1) the change in x by means of a notation Delta, thus Delta x = x_(2) - x_(1) and Delta t = t_(2) - t_(1). The average velocity bar(V) = (x_(2) - x_(1))/(t_(2) - t_(1)) = (Delta x)/(Delta t) The resistive force suffered by a motor boat is proportional to v^(2), where v is instantaneous velocity. The engine was shut down when the velocity of the boat was v_(0). Find the average velocity at any time t.