The Physics of Head on Collisions and Rear-End incidents:          Car accidents are horrible for different reasons. Simply looking at car accidents involving two people, there are just two basic types. The first is a head on collision, and the second is a rear-ending collisions. The effects of both of these can be looked at and analyzed by looking at the momentum of the vehicles, whether the collision is elastic or inelastic, and checking the conservation of momentum.                                                                                                                                                                                                                                                                                            Photo credit: https://plus.google.com/100809952271797514646/about         Lets start with a head on collision: The first step is to look at the momentum of each car. So lets say that the cars are moving towards each other at a constant speed of 30 m/s. One has a mass of 2kg, the other has a mass of 1kg (for easy calculation). The first thing that you will need to do is determine which is in the positive direction and which is in the negative direction. Then, you determine the momentum of each car using P=m*v. This means that one has a momentum of 30kg*m/s, and the other has a momentum of -60kg*m/s. Now, assuming that this collision is inelastic, which, according to Physics for Scientists and Engineers: A strategic Approach, is when two objects collide and get stuck together, you can look at the conservation of momentum which states that P1+P2=Pf , which translates to m1 v1+m2v2=mf vf. When you put the numbers in, you get initial momentum is -30kg*m/s, and the final momentum will be the total mass of the two cars, 3, times the new velocity. This new velocity will be the initial momentum/the mass which is 3. So the final velocity is -10m/s.         Now you can look at this, and determine that the car with double the mass will hit hit with more momentum, and carry both itself and the smaller car at 10m/s in the direction is was traveling. This is why car crashes can be so devastation. It is all about the momentum and relative size and speed of the two cars. You can use these equations for any for of collision, the only difference in a completely elastic collision is that you P1+P2=P1f +P2f, where you have the two different velocities and masses because the cars go off in different directions, which in the case of a car is back in the direction that it came from. Photo credit: http://www.mwl-law.com/nationwide-subrogation/automobile-med-pay-and-pip-subrogation/         The second type of collision that occurs often is a rear-ending incident, which happens when one car is stopped and another car rams into the back of it. The calculation for this type of scenario is quite similar to the first calculation that we did, the only difference is that one of the for both elastic, and inelastic collisions, there will only be one initial momentum, because the velocity of the second car is 0. Much like before, the elastic collision will have two final momentum terms, and the inelastic collision will have one final momentum term, which will be equal to the original momentum term, giving it a lower velocity because it will have a combined mass of both cars.