Now assume the position of vehicle j at time t is given by , see figure(1) below

Fig(1) Position of the Vehicles

A good rule of thumb for following another vehicle at a safe distance is allowing you the length of a car for ten meter per hour (14.67) m/s.

When we are travelling in terms of function , we have

1.A

Where =length of the car (normaly of 15 feet) and =speed of jth vehicle.

Length of a vehicle, must be added to the separation between vehicles to give the spacing

We assume that each driver is able to follow (1.A) at each time t.

This means that the driver must accelerate (or decelerate) his vehicle according to ER -