Solving Car Accident Problem: Jeep Speeding?

[jared13]

Homework Statement

Fresh from CSI training, you are sent to the scene of an accident. A 1,600kg Jeep Cherokee is locked in a crumpled pile of metal with what used to be a 900kg Chevy convertible. A witness tells you that the convertible was waiting at the light when the Jeep had hit its brakes and slid into the convertible, whereupon the convertible was crushed and the Jeep and convertible slid locked together until they came to rest. The witness also tells you that that at the time of the accident, the road surface was dry, just as it is when you arrive. After making some measurements, you determine that the coefficient of sliding (kinetic friction) beween the vehicle tires and the dry roadsurface is about .45. You also measure skid marks 23m in length on the road behind where the convertible was hit, and another 13m of skidmarks clearly form the jeep and convertible as they slid through the traffic light locked together. You check the road signs and see that the speed limit on that section of road is 45mph. Was the jeep speeding before it hit its brakes? (If so by how much?)

Homework Equations

F=ma
x=x0+v0xt+1/2axt^2
v=v0x+axt
v^2x=v0x^2+2axx

The Attempt at a Solution

Please help me I really don't know where to begin. If I had to take a guess I would say the coefficent of friction and the length of the skid marks has something to do with being able to judge how fast the car was going, but I do not not how they are linked.

Thanks for your help in advance!

 

[mgb_phys]

Conservation of energy.
At the start you have kinetic energy of the jeep.
All this is converted into friction (if you assume the bang lost no energy!)

Remember energy is force * distance,
How o you work out frictional force?

 

[kerimek]

As a scientist, my first step would be to gather all the necessary data and information. From the given information, we know the mass of the vehicles, the coefficient of sliding friction, and the length of the skid marks. We also know that the road surface was dry and the speed limit in that area is 45 mph.

Next, I would use the equations of motion to calculate the initial velocity of the Jeep before it hit its brakes. We can use the equation v^2 = v0^2 + 2ax to solve for v0, where v is the final velocity, v0 is the initial velocity, a is the acceleration (which in this case is due to friction), and x is the distance traveled (in this case, the length of the skid marks).

Plugging in the values, we get v0 = √(2ax) = √(2*0.45*23) = 6.32 m/s.

Now, we can convert this to mph by multiplying by 2.237 (1 m/s = 2.237 mph), giving us an initial velocity of approximately 14.15 mph.

Since the speed limit is 45 mph, we can conclude that the Jeep was not speeding before it hit its brakes. In fact, it was going significantly below the speed limit.

However, this does not necessarily mean that the Jeep was not at fault for the accident. There could have been other factors at play, such as the driver of the Jeep not paying attention or not braking in time. More investigation and analysis would be needed to determine the exact cause of the accident.