At the instant a motorbike starts from rest in a given direction, a car overtakes the bike, both moving in the same direction as shown in figure. The speed-time graphs for motor bike and car are represented by OAB and CD respectively.Then,

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at t = 18 s, the motor bike and car are 180 m apart

at t = 18 s, the motor bike and car are 720 m apart

the relative distance between motor bike and car reduces to zero at t = 27 s and both are 1080 m far from origin

the relative distance between motor bike and car always remains same

answer is C.

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Detailed Solution

Distance travelled by motor bike at t = 18 ss1=12×18×60=540mDistance travelled by the car at t = 18 sS2 = 18 x 40 =720mThe separation between motor bike and car at t = 18 s is 720 - 540 = 180 mLet the separation between them decreases to zero at time t beyond 18 s. Hencesbike =540+60t and scar =720+40t∴scar −sbike=0Therefore,720 + 40 t = 540 + 60 tSolving we get, t = 9 s beyond 18 stotal time = 18 + 9 = 27 s from the start.Distance travelled by both sbike + scar = 1080 m

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