car will overtake bike after 35  secExplanation:The distance from starting point, where bike reaches it final speed 10 m/s is given by    V2 = 2×a×S ; hence S = v2/(2a) = 100/2 = 50 m  TIME t1 for the bike to reach final velocity = v/a = 10/1 = 10 s.    The distance from starting point, where car reaches it final speed 15m/s is given by    v2 = 2×a×S ; hence S = v2/(2a) = 225/(2×0.5) = 225 m ................................(1)  Time t2 for the car to reach final velocity = v/a = 15/0.5 = 30 s.  In this 30 s duration of car travel, distance travelled by bike = Initial 50 m in 10 s + distance travelled in 20 s with uniform speed 10 m/s  = 50 + 20×100 = 250 m ............................(2)  From (1) and (2), we know that after 30 s the distance between car and bike = 25 m.  After 30 s , both bike and car are moving with uniform speed. Car speed is 15 m/s and bike speed is 10 m/s. hence additional time to cover this 25 m gap = 25/(15-10) = 5 s.  total time is 30+5 = 35 s.  Car will overtake bike after 35 s