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A highway motorist travels at a constant velocity of 45 km/h in a 30 km/h zone.A motor cyclist police officer has been watching from behind a bill board and at the same moment the speeding motorist passes the bill board, the police officer accelerates uniformly from rest to overtake her.If the acceleration of the police officer is 10 km/h^-2,how long does he take to reach the motorist? |
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Answer» Answer: Answer: Explanation: A HIGHWAY motorist travels at a constant velocity of 45 km/h in a 30 km/h zone. => Suppose, motorist travels at a constant velocity 'V'. V = 45km/h = 45*1000/3600 = 125 m/s [because 1km = 1000m and 1 hr = 3600 s] => motorist TAKES 't' time to cover the distence 'd'. ∴ v = d/t d = vt d = 12.5*t ...(1) => The police officer accelerates uniformly from rest to OVERTAKE her. the acceleration of the police officer = 10 km/h^² = 10*1000/(3600)² = 0.00077 m/s² => now, we can calculate the time by using below equation: d = ut + 1/2 at² 12.5t = 0 + 1/2 * 0.00077 * t² t = 12.5*2 / 0.00077 t = 32467.5 s t = 9.01 min Thus, the police officer takes 9.01 min to reach the motorist. |
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