Starting from rest, a car travels 1 350 meters in 1.00 minute. It accelerated at

Question

Starting from rest, a car travels 1 350 meters in 1.00 minute. It accelerated at 1.0 m/s2 until it reached its cruising speed. Then it drove the remaining distance at constant velocity. What was its cruising speed?

Explanation / Answer

Let the cruising speed is v m/s, Let it take t1 sec to reach v m/s,than:- 1st Phase:- By v = u + at =>v = 0 + 1 x t1 =>v = t1 ---------------(i) By s = ut + 1/2at =>s1 = 0 + 1/2 x 1 x t1^2 =>s1 =1/2 x t1^2 ------------(ii) 2nd Phase:- t2 = 60-t1 & s2 = 1350 - 1/2 x t1^2 By distance = velocity x time =>s2 = v x t2 =>1350 - 1/2 x t1^2 = t1 x (60-t1) =>1350 - 1/2 x t1^2 = 60t1 - t1^2 =>1/2 x t1^2 -60t1 +1350 = 0 =>t1^2 -120t1 + 2700 = 0 =>t1 = [-(-120) +/- sqrt{(-120)^2 - 4 x 1 x 2700)}]/(2 x 1) =>t1 = [120 +/- 60]/2 =>t1 = 90 or 30 sec [but t1 can not be equal to 90 sec] =>t1 = 30 sec =>v = 30 m/s is its cruising speed

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