You are called as an expert witness to analyze the following auto accident

Analysis of Auto Accident

You are called as an expert witness to analyze the following auto accident: Car B, of mass 2000 kg, was stopped at a red light when it was hit from behind by car A, of mass 1300 kg. The cars locked bumpers during the collision and slid to a stop. Measurements of the skid marks left by the tires showed them to be 7.25 m long, and inspection of the tire tread revealed that the coefficient of kinetic friction between the tires and the road was 0.65.

a) What was the speed of car A just before the collision?

b) If the speed limit was 35mph, was car A speeding, and if so, by how many miles per hour was it exceeding the speed limit?

c) Explain why we can classify the collision as completely inelastic

d) Calculate the total kinetic energy before and after the collision

a) What was the speed of car A just before the collision? b) If the speed limit was 35mph, was car A speeding, and if so, by how many miles per hour was it exceeding the speed limit? c) Explain why we can classify the collision as completely inelastic d) Calculate the total kinetic energy before and after the collision

a). va=17.23 𝑚s or 38.54 mph b). v=38.54 mph and limit is 35 mph c). Completely inelastic d). Eka=192.967 kJ Ekt=76.071 kJ Explanation: 𝑚𝑎=1300kg 𝑚𝑏=2000kg 𝑥𝑓=7.25m 𝑢𝑘=0.65 The motion is an inelastic collision so 𝑚𝑎*𝑣𝑎+𝑚𝑏*𝑣𝑏=(𝑚𝑎+𝑚𝑏)*𝑣𝑓 The force of the motion is contrarest by the force of friction so F-F𝑢𝑘=0 F=F𝑢𝑘 F𝑢𝑘=𝑢𝑘*𝑚*𝑔 F=m*a a=Fm a=𝐹𝑢𝑘𝑚 a=𝑢𝑘*𝑔 a=0.65*9.89.8𝑚𝑠2 a=6.39𝑚𝑠2 Now with the acceleration can find the time and the velocity final that make the distance 7.25m being united 𝑥𝑓=𝑥𝑜+𝑣𝑜*𝑡+2*𝑎*𝑡2 𝑥𝑜=0 𝑣𝑜=0 𝑥𝑓=2*𝑎*𝑡2 𝑡2=𝑥𝑓2*𝑎 𝑡=𝑠𝑞𝑟𝑡7288𝑚6.39𝑚𝑠2 𝑡=1.06s So the velocity final can be find using this time 𝑣𝑓=𝑣𝑜+𝑎*𝑡 𝑣𝑜=0 𝑣𝑓=6.39𝑚𝑠2*1.06𝑠 𝑣𝑓=6.79 𝑚𝑠

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