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Motion In A Plane

Question
CBSEENPH11020723

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s1 and that covered in the first 20 s is s2, then

  • s2 = 2s1

  • s2 = 3s1

  • s2 = 4 s1

  • s2 = s1

Solution

C.

s2 = 4 s1

If the particle is moving in a straight line under the action of a constant force then distance covered s = ut + at2 /2
since the body start from rest u = 0
therefore, s = at2/2
Now,
straight s subscript 1 space equals 1 half straight a left parenthesis 10 right parenthesis squared space space space space.... space left parenthesis straight i right parenthesis
and space
straight s subscript 2 space equals space 1 half space straight a space left parenthesis 20 right parenthesis squared space.... space left parenthesis ii right parenthesis
Dividing space eq space left parenthesis straight i right parenthesis space and space eq space left parenthesis ii right parenthesis comma space we space get

straight s subscript 1 over straight s subscript 2 space equals space fraction numerator left parenthesis 10 right parenthesis squared over denominator left parenthesis 20 right parenthesis squared end fraction

straight s subscript 2 space equals space 4 straight s subscript 1