# Crash reconstruction question

## Main Question or Discussion Point

What formula(s) would I use to find the initial velocity of a vehicle that has impacted a second vehicle in a same direction crash. There are no tire marks on the roadway and no braking involved. Thanks.

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In physics, there is something called translation symmetry, meaning that the fundamental properties of the Universe does not depend on where you are. Out of this symmetry, a phenomena known as momentum arises. In non-relativistic velocities, this is a good approximation.

From your post, I assume that the first car (called car A) hits the second car (car B) from behind. No matter if some kinetic energy is converted to heat energy via friction, the sum of the momentum for car A and the momentum of car B before the impact is the same as the sum of the momentum for car A and the momentum for car B after the impact.

$$m_{A(before)} v_{A(before)} ~+~ m_{B(before)}v_{B(before)}~ = m_{A(after)} v_{A(after)} ~+~ m_{B(after)} v_{B(after)}$$

Solve for the velocity for A before the crash if you have access to the other values.

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In physics, there is something called translation symmetry, meaning that the fundamental properties of the Universe does not depend on where you are. Out of this symmetry, a phenomena known as momentum arises. In non-relativistic velocities, this is a good approximation.

From your post, I assume that the first car (called car A) hits the second car (car B) from behind. No matter if some kinetic energy is converted to heat energy via friction, the sum of the momentum for car A and the momentum of car B before the impact is the same as the sum of the momentum for car A and the momentum for car B after the impact.

$$m_{A(before)} v_{A(before)} ~+~ m_{B(before)}v_{B(before)}~ = m_{A(after)} v_{A(after)} ~+~ m_{B(after)} v_{B(after)}$$

Solve for the velocity for A before the crash if you have access to the other values.
I don't have the values for pre collision velocity on either vehicle. How can I determine this? A wall was impacted after the two vehicles became stuck together and after impact with the wall vehicle two separated and rolled over and skid to a stop 40 feet after separation on it' s roof.

In non-relativistic velocities, this is a good approximation.
Translation symmetry only exists in the Newtonian limit?!?