When a particle moves in a circle with a speed u, its instantaneous velocity has a magnitude u and its direction is along

tangent at the point. The direction of the instantaneous velocity keeps changing by centripetal force which is acting as tension in the string here. Now at the instant when string breaks, this force disappears and the direction of the instantaneous velocity of the particle can no longer change. Hence the particle moves along the tangent direction

at that point on the circle.