A van starts moving with constant acceleration of 2 ms–2. A motorbike starts towards the van with a constant velocity of 20 ms–1. If the motorbike was 96 m behind the van at the start. Find the time in which motorbike will overtake the van.
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Explanation:
Vof bus V
b
=0 , Velocity of cyclist V
c
=20m/s,
Acceleration of bus a
b
=2m/s
2
Acceleration of cyclist a
c
=0
Relative velocity V
cb
=V
c
−V
b
=20m/s
Relative acceleration a
cb
=a
c
−a
b
=−2m/s
2
Relative separation =96m
Using s=ut+
2
1
at
2
⇒96=20t−
2
1
2t
2
⇒t
2
−20t+96=0
Solving the equation , we get t=8s and t=12s
Hence, after 8s, cyclist will overtake the bus.
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