A bus starts moving with acceleration 2 text m/s2 . 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?

Question

A bus starts moving with acceleration 2 text m/s2 . 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

Tardigrade Admin · Accepted Answer

Let the cyclist overtake the bus after time t. Then, 20× t=96+(1/2)× 2× t2 or t2-20t+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.

Q. A bus starts moving with acceleration $2 m / s^{2}$ . 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?

$4 s$

$8 s$

$12 s$

$16 s$

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

Q. A bus starts moving with acceleration 2m/s2 . 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?

4s

8s

12s

16s