Two cars are travelling on a straight road. The car c1 is going at a constant speed of 9m/s. 40 metres ahead of c1, car c2 initially at rest, but starts moving at an acceleration of 1m/s^2.During their motion, the car c1 overtakes c2, but soon c2 overtakes c1. Determine the maximum lead that c1 can have from c2:

a) 0.5m   b)9.5m   c)81m  d)90m

Dear Student,

Please find below the solution to the asked query:

If the separation between the C1 and C2 is maximum, then the difference of the first car displacement and the displacement of the second car displacement should have its maximum value. Therefore,

 S1=9tS2=12×1×t2So, the difference is,S=S1-S2=9t-t22For this to be maximum,dSdt=0ddt9t-t22=09-t=0t=9 sec.So,S=9×9-922=40.5 mTherefore, initially the first car is 40 m behind the second car.Therefore the maximum lead is 0.5 m

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