A traffic accident occurred in a 35 km/hr speed limit zone on Millway Street in which a 3000-kg Cadillac Escalade SUV rear-ended a 2000-kg Subaru Outback Wagon that was stopped at a stop sign. Because the entire police investigative division has gone on vacation to Bora Bora to relax, the mayor has contracted my team of experts to determine what happened and what traffic laws were broken. Using the little bit of data we were supplied we were able to find out enough information to figure out if the driver of the 3000-kg Cadillac Escalade SUV was speeding.
Using our kinematics equations we used the formula Vf^2 = Vi^2 + 2ad to figure out the velocity of both the Wagon and the SUV. Using the skid marks we were able to determine the distance and we were given acceleration. On top of that we knew the final velocity had to be zero because the cars came to a complete stop. Using what we knew we solved for Vi and found that the SUV’s initial velocity was 2.8 m/s and the wagon’s initial velocity was 12 m/s. Since we found the velocity of both vehicles and the masses were given we were able to use the equation mv = p to calculate the momentum of both immediately following the collision. We found that the momentum of the SUV equaled a total of 8,400 kg*m/s and the wagon equaled 24,000 kg*m/s. Knowing that the momentum before the collision has to be equal to the momentum after the collision we were able to find the momentum of each vehicle immediately before the collision. We added up each cars momentum from after the collision and got a total of 32,400 kg*m/s but, because the wagon was sitting at a stop sign it had no momentum therefore the SUV had a momentum of 32,400 kg*m/s.
After finding the momentum of the cars before the collision we used the equation mv = p to calculate the speed/velocity before the cars collided. Using the given mass of 3000kg and the momentum of 32,400 kg*m/s we found the speed/velocity was 10.8 m/s for the SUV. The speed of the wagon had to be 0 because it was sitting still at the stop sign. Using what we know about conversions we were able to convert 10.8 m/s to km/hr finding out that the SUV was going 38.88 km/hr which was three km/hr over the speed limit. Therefore the SUV was indeed speeding.