Question

# A bus starts moving with acceleration 2 ms−2. A cyclist 96 m behind the bus starts simultaneously toward the bus at a constant speed of 20 m/s. After some time, the bus will be left behind. If the bus continues moving with the same acceleration, after what time from the beginning, the bus will overtake the cyclist?

A
10 s
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B
12 s
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C
14 s
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D
16 s
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Solution

## The correct option is B 12 sLet at time t, the cyclist overtakes the bus, then 96+(distance travelled by bus in time t)=(distance travelled by cyclist in time t) ⇒12×2×t2+96=20×t ⇒t2−20t+96=0 This gives, t=8 s or 12 s Hence, the cyclist will overtake the bus at 8 s And then the bus overtakes the cyclist at 12 s.

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