Was the Driver Really Traveling Under 15 km/hr?

[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.

(Possible?) Equations:

fkinetic = (µkinetic)(n)
(µkinetic)=kinetic friction coefficient
n= m*g

m1 v1i + m2 v2i = m1 v1f + m2 v2f
and
1/2 m1 v1i2 + 1/2 m2 v2i2 = 1/2 m1 v1f2 +1/2 m2 v2f2
(am I missing any equations ?)


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 know that the answer is supposed to be 23.3km/hr, and that the driver was not telling the truth.

 

[kerimek]

Hello there! It seems like you have a good understanding of the equations involved in this problem. To find the speed of the cars just after the collision, you can use the equation m1v1i + m2v2i = m1v1f + m2v2f, as you mentioned. This equation states that the initial momentum of the two cars (before the collision) is equal to the final momentum (after the collision).

To solve for the initial velocity, you will need to know the final velocity of the cars, which can be calculated using the conservation of kinetic energy equation: 1/2 m1v1i^2 + 1/2 m2v2i^2 = 1/2 m1v1f^2 + 1/2 m2v2f^2.

Once you have the final velocity, you can plug it into the first equation and solve for the initial velocity. This will give you the speed of the cars just after the collision.

As for converting meters to kilometers, you can use the conversion factor 1 meter = 0.001 kilometers.

Using the given information about the skid marks and the frictional coefficient, you should be able to calculate the final velocity and determine if the driver's claim of traveling less than 15 km/hr is true. I hope this helps guide you in the right direction. Good luck on your exam!