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Question

The driver of a car moving with a speed of 10 m s to the power of negative 1 end exponent sees a red light ahead, applies breaks and stops after covering 10m distance. If the same car were moving with a speed of 20 blank m s to the power of negative 2 end exponent, the same driver would have stopped the car after covering 30 m distance. Within what distance the car can be stopped if travelling with a velocity of 15m s to the power of negative 1 end exponent ? blankAssume the same reaction time and the same deceleration in each case.

  1. 18.75 m  
  2. 20.75 m  
  3. 22.75 m  
  4. 25 m  

The correct answer is: 18.75 m


    If t subscript 0 end subscriptis the reaction time, then the distance covered during decelerated motion is 10 minus 10 t subscript 0 end subscript.
    Now, in the first case,
    10 to the power of 2 end exponent equals 2 a left parenthesis 10 minus 10 t subscript 0 end subscript right parenthesis (i)
    Similarly, in the second case,
    20 to the power of 2 end exponent equals 2 a left parenthesis 30 minus 20 t subscript 0 end subscript right parenthesis (ii)
    Again, in the third case,
    15 to the power of 2 end exponent equals 2 a left parenthesis x minus 5 t subscript 0 end subscript right parenthesis.(iii)
    Dividing Eq.(ii) by Eq. (i),fraction numerator 20 to the power of 2 end exponent over denominator 10 to the power of 2 end exponent end fraction equals fraction numerator 30 minus 20 t subscript 0 end subscript over denominator 10 minus 10 t subscript 0 end subscript end fraction
    or 40 minus 40 t subscript 0 end subscript equals 30 minus 20 t subscript 0 end subscript
    or 20 t subscript 0 end subscript equals 10 or t subscript 0 end subscript equals fraction numerator 1 over denominator 2 end fraction s
    Dividing Eq. (iii) by Eq. (i), we get
    fraction numerator 225 over denominator 100 end fraction equals fraction numerator x minus 15 t subscript 0 end subscript over denominator 10 minus 10 t subscript 0 end subscript end fraction or fraction numerator 9 over denominator 4 end fraction equals fraction numerator x minus 15 cross times fraction numerator 1 over denominator 2 end fraction over denominator 10 minus 10 cross times fraction numerator 1 over denominator 2 end fraction end fraction
    45 equals 4 x minus 30 or 4 x equals 75
    or x equals fraction numerator 75 over denominator 4 end fraction m equals 18.75m

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