A bus starts moving with acceleration 2 m/s². A cyclist 96 m behind the bus starts simultaneously towards the bus at 20 m/s. After what time will he be able to overtake the bus?(a) 4 sec (b) 8 sec(c) 12 sec(d) 16 sec
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answer should be 8 second
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Answer:
C) 12 seconds
Explanation:
Acceleration of bus = 2 m/s²
Disance of cyclist is 96m behind the bus starts biking simultaneously towards the bus at 20 m/s.
Lets suppose the position of the cyclist to be "0" (t= 0)
The position of the bus = 96 + a t² = 96 + t²
The position of the cyclist = Vt = 20 t
Therefore where they will meet ⇒ 20 t = 96 + t²
Thus,
t² - 20 t + 96 = 0
= (20 +- 4) /2
The cyclist passes the bus at (20 - 4) /2 = 8 s
Therefore, the bus will overtake the cyclist at (20+4)/2 = 12 s
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