A police car going 25 mph spots a speeding car going at 85 mph and 200 feet ahea

Question

A police car going 25 mph spots a speeding car going at 85 mph and 200 feet ahead of him. The police car accelerates at 25 ft/s2. The reaction time of the police car is 0.8 seconds. How many total seconds will it take the police to reach the speeding car and how many miles from his/her starting position will the police car have traveled by the time he reaches the speeding car and what is the police car's velocity? Answer the same questions, if 2 seconds after the police accelerates, the speeding car also accelerates at 10 ft/s2. answers: Ttotal= 10.15 seconds. Xpolice = .278 miles. Vpolice= 184.38 mph, Vcar = 85 mph Ttotal= 13.03 seconds. Xpolice = -445 miles. Vpolice= 233.50 mph. Vcar = 154.76 mph

Explanation / Answer

1 foot = 0.0001893 miles hence 25mph = 36.68ft/s 85mph =124.73 ft/s in 0.8 sec distance =0.8*124.73 =99.78 ft in 0.8 sec disatnce covered by police =36.68*0.8 =29.344ft total difference between cars before police accelerates =200+99.78-29.34 =270.44 ft hence 124.73t +270.44 =36.68t+1/2 *25t^2...........1 hence t =9.35 sec Ttotal =9.35+0.8 =10.15 sec from 1 putting value of t we get X police =0.278 miles

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