Documentation:FIB book/problems/Accident Reconstruction

Assume a rear-end collision takes place on a T-crossing road. The insurance company tried to find out whether the driver was speeding at the intersection. From Figure 2, Vehicle 1(Blue Tesla Model 3) was rear end on the vehicle 2 (red). Vehicle 2 was stationary parked on the side of the road. The damage dimension is given by an accident reconstruction form (Figure 1). Assume A=800n/cm , B=80n/cm^2, Speed limit is 15m/h.

Figure 1. Accident reconstruction form

Figure 2. Collision track map

Question 1

Using the Barrier Equivalent Velocity method to find out the speed before the collision happened.

SOLUTION (expand to show)
According to the above formula, $tan\theta =(185-135)/1850=0.0058$ $1+tan\theta ^{2}=1.00003378$ $E=7403.44J$ $v=2.83m/s=10.192km/h$

Question 2

Give analysis on whether the driver was speeding or not at that time (consider the definition of BEV). 

SOLUTION (expand to show)

In this case, the calculations show that Tesla was not exceeding the speed limit of 15 km/s just before the collision. However, the definition of BEV is the Barrier Equivalent Velocity, which means the car stopped after the collision. Even though the change of velocity of theoretical value is the same as reality, the Tesla must have a higher speed before impact since it collides with a movable object. Therefore, we cannot make the conclusion that the driver was speeding at that time. Further investigation can be determined by energy conservation(no need to calculate ).

Question 3

Give a short summery about what types of the collision of the example and what injuries the driver might get.

SOLUTION (expand to show)
After reconstruct the accident, it is a low speed rear-end collision. In this type of frontal crash, occupants have a higher tendency to involve in a short term whiplash associated disorder, which caused by the rapid extension-flexion movement of the head. Skin laceration and bruises may cause by the seat belt restraint system.