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Question

A car is chasing a motorbike on a straight road. The car is going at its maximum speed v (assumed uniform). The person on motorbike started his ride when the car was at a distance d away from him, and the motorbike starts with constant acceleration a. What should be the condition for the speed of the car v, so that motorbike will be caught?

A
vad
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B
v2ad
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C
v2ad
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D
None of these
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Solution

The correct option is C v2ad
Given, speed of the car = v
Initial speed of the motorbike, u=0
Acceleration of the motorbike = a
Initial separation between car and motorbike = d
Let, the motorbike is caught at a time t after it starts. So, the distance travelled by the motorbike during this interval is
s=ut+12at2=0+12 at2=12at2................(i)
During this interval the car travels a distance s+d=vts=vtd.......................(ii)
From eq (i) and (ii) we have
12at2vt+d=0t=v±v22ada
The motorbike will be caught if time is real and positive. So, this is possible only when v22adv2ad

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