As already stated. The force of the impact is determined by the speed and mass of the two colliding objects. If you are both travelling at say 60 m.p.h and the car in front of you breaks slightly at say 59 m.p.h then the speed of the impact is of the velocity of 1 m.p.h as both are tarvelling at the same speed, both relative to the road.
One also has to consider varible vectors as the cars may not be travelling in exactly the same line.
Picture the cars being toy cars, both in a box and crash one into the other at around 1 m/p/h. Now take this box and sit in a car tarvelling 60 m/p/h. Mass is obviously different but the speed of impacty is still 1 m/p/h relative to the car you are sitting on.
If you, the observer in s sees an object moving along x axis at velocity (w), then you are the 'system (s).Transiting at velocity v in the specific direction x with respect to S (you), You will then see the object moving with the velocity w' where
We can therefore do a little math and change the equation....
Now that if that object was to move at SPL (speed of light) in the S system (e.g. w = c), it will too be shifting; S' system. Further more, if w & v were small in respect to SPL, we recover the Galilean transformation of velocities: .
To simplify ir fuether, (call the system k) travelling north with velocity v with respect to the road (system k). you inside the car throw a ball east with a velocity u in respect road (not your direction should the road bend). Classical physics state, the observer, standing still on the side of the road will measure V (of the ball) of the asv
+ U. Special relativity however proves this as incorrect. Instead, the person standing on the kerb will measure the velocity of the ball as . If u and v are small in comparison to c, then the v + U is valid