#### Thesis Title

The Relationship Between Energy Loss and Velocity Change in Analyzing Vehicle Collisions

Spring 2006

#### Degree

Master of Science in Mathematics

Mathematics

Bruno Schmidt

#### Keywords

velocity, acceleration, energy, force, mass

Mathematics

#### Abstract

In any type of collision between two vehicles, one of the goals of an accident reconstructionist is to determine the initial velocities of both cars. This helps to discern whether one or both of the cars were speeding, to discover the locations of the cars at the beginning of the hazardous situation, and if the accident could have been avoiding on someone’s part. The find the initial velocities, we must look at the immediate post collision velocities together with the momentum and energy principles. A common misconception among some reconstructionists is that the damage from only one automobile can be used to determine the collision forces, delta-v, energy loss, and momentum change of the vehicle. However, this simply is not the case, as this paper will discuss. In a collision, both vehicles have an initial velocity. By multiplying each vehicle’s mass and velocity, we acquire the momentum. This, as well as the crush factor of the two vehicles, determines the amount of damage to each vehicle. The moment the two cars touch, each car begins to experience a change in its momentum, energy, and velocity. As the vehicles push against each other, each exerts a force onto the other vehicle. At this same time, the cars experience deformation. The change in velocity for each car is known as delta-v. The amount of damage down to each car can be recreated by crashing the car into a solid barrier at a known speed, called Barrier Equivalent Velocity (BEV). Many reconstructionists incorrectly equate delta-v and BEV. This paper shows the difference between the two.