what is the applcation of force and motion on road safety?

There are many actually.
1. Seat belt. When accidents occur, seat belt lengthens the impact time. By F = (mv-mu)/t, longer impact time reduces force on the passengers. It hurts less.
2. Stopping distance = thinking distance + braking distance. When the driver sees something in front of the car, he will brake. But before he brakes, he has a reaction time (normally 0.2 seconds). During his reaction time, the car travels at its initial velocity. So thinking distance = reaction time x initial velocity. If the driver initially drives at high speed, the thinking distance is longer. There will be less time for the driver to brake. Accidents happen more easily.