This paper considers the case of two vehicles crossing an intersection from perpendicular directions. A second-order kinematic model is assumed as well as that initially both vehicles move with their maximum permissible speed. A braking/reaccelerating speed profile is proposed for the vehicle crossing second that enables it to brake without colliding with the first even if the latter unexpectedly and immediately comes to a stop. Under the aforementioned constraint, the time loss incurred by the second vehicle due to braking is used as an optimization criterion. When the profile that leads to this minimum delay is not unique, the maximum deceleration applied is used as a secondary criterion. The problem is solved analytically providing closed-form solutions.