Question

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

• A. 4 s
• B. 8 s
• C. 12 s
• D. 16 s

Answer 1

Answer: (B)

Let at time $t$ , the cyclist overtakes the bus, then $96+$ (distance traveled by bus in time $t$) = (distance traveled by cyclist in time $t$)

$\Rightarrow \frac{1}{2}\times 2\times 2\times t^2+96=20\times t$

$\Rightarrow t^2-20t+96=0$

This gives, $t=8s$ or $12s$.

Hence, the cyclist will overtake the bus in $8s$