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Question
Two cars leave with a time gap of 1 minute from the same point. They move with an acceleration of 0.2 m/s2. How long after the departure of the second car, does the distance between them become equal to three times its value, when the second car just starts?
Two cars leave with a time gap of 1 minute from the same point. They move with an acceleration of 0.2 m/s2. How long after the departure of the second car, does the distance between them become equal to three times its value, when the second car just starts?
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Solution
car1 start from rest and drives 60 s => s = at²/2 = 0.2*60²/2 = 360 m
car 2 starts when car 1 has driven 360 m.
car 1 drives s1 = a(t + 60)²/2
car 2 drives s2 = at²/2
The diffence s1 - s2 = 3* 360 = 1080
a(t+60)²/2 - at²/2 = 1080
(t+60)² - t² = 2160/a
120t + 3600 = 2160/0.2 = 10800
t = (10800-3600)/120 = 60
car 2 starts when car 1 has driven 360 m.
car 1 drives s1 = a(t + 60)²/2
car 2 drives s2 = at²/2
The diffence s1 - s2 = 3* 360 = 1080
a(t+60)²/2 - at²/2 = 1080
(t+60)² - t² = 2160/a
120t + 3600 = 2160/0.2 = 10800
t = (10800-3600)/120 = 60
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