Question

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

Answer 1

answer should be 8 second

Answer 2

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