Question

A bus starts moving with acceleration $ 2\text{ }m/{{s}^{2}} $ . A cyclist 96 m behind the bus starts simultaneously towards the bus of 20 m/s. After what time will he be able to overtake the bus?

• A. $ 4s $
• B. $ 8s $
• C. $ 12s $
• D. $ 16s $

Answer 1

Answer: (B)

Let the cyclist overtake the bus after time t. Then, $ 20\times t=96+\frac{1}{2}\times 2\times {{t}^{2}} $ or $ {{t}^{2}}-20t+96=0 $ or $ (t-12)(t-8)=0 $ or $ t=8\text{ }s $ and $ 12s $ Thus, the cyclist will overtake the bus after 8 s.