A common form of pedestrian accident involves the pedestrian emerging from behind a stopped vehicle, into the path of an oncoming car. A mathematical model (“EMERGE”) has been developed for calculating the time available to the driver to see and avoid the pedestrian. It involves calculating in 2 dimensions the equations of motion of the vehicle and the pedestrian, together with the lines of sight of the driver and the pedestrian around the stopped vehicle. The sensitivity of the model to the different variables is demonstrated.The model allows for deceleration of the car. For any given driver perception-reaction time and car deceleration rate, the model can be used to calculate the maximum speed of the car from which it would have been possible to have avoided the collision by braking to a stop. This can often demonstrate that the driver would only have been able to have avoided the collision if he had driven at an unreasonably low speed.The model also has application in some vehicle-to-vehicle and bicycle-to-vehicle collisions where vehicles are hidden from each other until just before the collision.