i tried equaling to each other but cant seem to get the answer! A police car goi

Question

i tried equaling to each other but cant seem to get the answer!
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/s^2. 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/s^2.

Explanation / Answer

25 mph = 11.17 m/s, 85 mph = 37.99 m/s, 200 ft = 60.96 m, 25ft/s^2 = 7.62 m/s^2 Let after t time the police catches the car after the reaction time so s = 11.17t+.5*7.62*t^2 also in reaction time it travels = 11.17*.8 m = 8.936 m distance traveled by car in this time (t+.8) = 38 * (t+.8) = 38t + 30.4 so 11.17t+.5*7.62*t^2 + 8.936 - 38t + 30.4 = 200 (given initial distance) simplifying 3.81t^2 - 26.83t - 160.664 = 0 solving for t we get t = 10.91 sec so it will take a total of (10.91 + .8) sec = 11.71 sec for police car to catch the car Distance traveled from the starting position = 11.17t+.5*7.62*t^2 + 8.936 putting value of t and solving we get distance = 584.297 m = .363 miles speed of the police car v = u + at = 11.17 + 7.62*10.91 = 94.304 m/s = 210.95 mph method of solving will be similar just instead of constant speed of car accelerate if after 2 sec of police accelerating. If you feel doubt in doing that feel free to contact. Do rate! :)

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