Physics-
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Question

A particle starts from rest and experiences constant acceleration for 6 s. if it travels a distance d subscript 1 end subscript in the first two second, a distance d subscript 2 end subscript in the next two seconds and a distance d subscript 3 end subscript in the last two second, then

  1. d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 1 blank colon 1  
  2. d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 2 blank colon 3  
  3. d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 3 blank colon 5  
  4. d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 5 blank colon 9  

The correct answer is: d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 3 blank colon 5


    Let particle start from O and travels distance
    d subscript 1 end subscript open parentheses O A close parentheses comma blank d subscript 2 end subscript open parentheses A B close parentheses comma blank d subscript 3 end subscript open parentheses B C close parentheses
    From equation of motion, we have
    s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent

    F o r blank O A blank colon blank t equals 2 blank s comma blank u equals 0
    d subscript 1 end subscript equals fraction numerator 1 over denominator 2 end fraction a open parentheses 2 close parentheses to the power of 2 end exponent equals 2 a
    F o r blank O B blank colon blank t equals 4 blank s comma blank u equals 0
    therefore blank s subscript 2 end subscript equals fraction numerator 1 over denominator 2 end fraction a open parentheses 4 close parentheses to the power of 2 end exponent equals 8 a
    d subscript 2 end subscript equals 8 a minus 2 a equals 6 a
    F o r blank O C blank colon blank t equals 6 blank s comma blank u equals 0
    therefore blank S equals fraction numerator 1 over denominator 2 end fraction a open parentheses 6 close parentheses to the power of 2 end exponent equals 18 a
    Distance in last 2 blank s equals 18 a minus 8 a equals 10 a
    therefore blank d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 2 a blank colon 6 a blank colon 10 a
    d subscript 1 end subscript blank colon d subscript 2 end subscript blank colon d subscript 3 end subscript equals 1 blank colon 3 blank colon 5

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