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Question

A the instant a motor bike starts from rest in a given direction, a car overtakes the motor bike, both moving in the same direction. The speed-time graphs for motor bike and car are represented by O A B and C D respectively Then

  1. At t equals 18 s the motor bike and car are 180m apart    
  2. At t equals 18 s the motor bike and car are 720m apart    
  3. The relative distance between motor bike and car reduces to zero at t equals 27 s and both are 1080m far from origin    
  4. The relative distance between motor bike and car always remains same    

The correct answer is: The relative distance between motor bike and car reduces to zero at t equals 27 s and both are 1080m far from origin


    Distance travelled by motor bike at t equals 18s
    s subscript b i k e end subscript equals s subscript 1 end subscript equals fraction numerator 1 over denominator 2 end fraction(18)(60)=540 m
    Distance travelled by car at t equals 18s
    s subscript c a r end subscript equals s subscript 2 end subscript=(18)(60)=720 m
    Therefore, separation between them at t equals 18s is 180m. Let, separation between them decreases to zero at time t beyond 18s.
    Hence, s subscript b i k e end subscript equals 540 plus 60 t and s subscript c a r end subscript equals 720 plus 40 t
    s subscript c a r end subscript minus s subscript b i k e end subscript equals 0
    rightwards double arrow blank 720 plus 40 t equals 540 plus 60 t
    rightwards double arrow blank t equals 9s beyond 18s or
    Hence, t equals open parentheses 18 plus 9 close parenthesess=27s from start and distant travelled by both is s subscript b i k e end subscript=s subscript c a r end subscript equals 1080m

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