# Elastic Collision of Two cars

#### KrispyKrunch

Hey there! So, I've got this sample exam that I'm working my way through, and I'm stuck on a few questions, but this one is particularly frustrating me:

A careless driver rear-ends a car that is stopped at an intersection. Just before the collision, the driver slams on his brakes, locking the wheels. The mass of the struck car also has his foot on the brake pedal, locking the wheels. The mass of the struck car is 900kg, and that of the initially moving car is 1200Kg. On collision, the bumpers of the two cars mesh. Police determines from skid marks that after the collision the two cars moved 0.76metres together, straight into the intersection. Tests revealed that the frictional coefficient of kinetic friction between the tires and pavement was 0.92. The driver of the moving car claims that he was traveling less than 15 km/hr as he approached the intersection. Is he telling the truth? Hint find the speed of the cars just after the collision first.

Ok, so to start, I don't know how to get the speed? I'm assuming you would first change the meters into Km, but I honestly don't know how to get the speed! I know that once I get the initial velocity, I can use the elastic collision formula to figure out the final velocity(or is it the other way around?) If you could point me in the right direction that would be fantastic! Thanks!!

#### KrispyKrunch

Also, I forgot to mention, the answer is 'The speed of the car was 23.3 km/hr. He was not telling the truth"

#### physicsquest

PHF Helper
The collision in this case is ineleastic as the the bumpers of the two cars mesh and then they travel as one body.

Assume the vel of this combination is V. Find the K.E. This K.E. is used up in doing work against force of friction. (F.s).

Once you have V, work backwards and apply conservation of momentum to find the initial speed.