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Question

A particle starting from rest falls from a certain height. Assuming that the value of acceleration due to gravity remains the same throughout motion, its displacement in three successive half second intervals are S subscript 1 end subscript blank comma S subscript 2 end subscript comma blank S subscript 3 end subscript.
Then,

  1. S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript colon 1 colon 5 colon 9  
  2. S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript colon 1 colon 2 colon 3  
  3. S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript colon 1 colon 1 colon 1  
  4. S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript colon 1 colon 3 colon 5  

The correct answer is: S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript colon 1 colon 3 colon 5


    (S to the power of ´ end exponent proportional to t to the power of 2 end exponent. Now, S subscript 1 end subscript superscript ´ end superscript colon S subscript 2 end subscript superscript ´ end superscript colon S subscript 3 end subscript superscript ´ end superscript ∷ fraction numerator 1 over denominator 4 end fraction colon 1 colon fraction numerator 9 over denominator 4 end fraction or 1:4:9
    For successive intervals,
    S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript ∷ 1 colon open parentheses 4 minus 1 close parentheses colon left parenthesis 9 minus 4 right parenthesis
    o r blank S subscript 1 end subscript colon S subscript 2 end subscript colon S subscript 3 end subscript ∷ 1 colon 3 colon 5

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