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A car is travelling with a constant speed of 80km/h and passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80km/h in 10 seconds reaching a constant speed of 100 km/h after a further 5 seconds. At what time will the policeman catch up with the car?
IT IS 17.5 S
Car travels at 80km/h (22.222m/s).Car would have travelled 333.333m after 15 seconds.Bike sets off from rest to 80km/h (22.222m/s) in 10s. This is acceleration of 2.222m/s².Then from 80km/h (22.222m/s) to 100km/h (27.778m/s) in 5s. This is acceleration of 1.111m/s².Distance travelled in first acceleration is (s=ut+½at²)s1 = 0 + ½*2.222*10²s1 = 111.111mDistance travelled in second acceleration is (s=ut+½at²)s2 = 22.222*5 + ½*1.111*5²s2 = 125mTotal distance travelled in 15s by the bike is thens1 + s2 = 236.111mWhich is 333.333m - 236.111m = 97.222m from the car in the first 15s.The bike advancing at 20km/h (5.556m/s) to the car which would take anothert = s/v = 97.222 / 5.556 = 17.50sto catch up.Total time is therefore 15 + 17.5 = 32.50s
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