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Motion In Straight Line

Question
CBSEENPH11020564

A particle is moving such that its position coordinates (x,y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2 sec and (13 m, 14m) at time t= 5 sec. Average velocity vector (vav) from t = 0 to t = 5 s is,

  • 1 fifth left parenthesis 13 space i with hat on top space plus space 14 space j with hat on top right parenthesis
  • 7 over 3 open parentheses i with rightwards arrow on top space plus space j with hat on top close parentheses
  • 2 space left parenthesis straight i with hat on top space plus space straight j with hat on top right parenthesis
  • 11 over 5 open parentheses i with hat on top plus j with hat on top close parentheses

Solution

D.

11 over 5 open parentheses i with hat on top plus j with hat on top close parentheses

Average velocity vector,

straight v subscript av space equals space fraction numerator Net space displacement over denominator Time space taken end fraction

space space space space space space equals space fraction numerator left parenthesis 13 minus 2 right parenthesis straight i with hat on top space plus space left parenthesis 14 minus 3 right parenthesis straight j with hat on top over denominator 5 end fraction

space space space space space space equals space fraction numerator 11 space straight i with hat on top space plus space 11 space straight j with hat on top over denominator 5 end fraction

space space space space space space space equals space 11 over 5 open parentheses straight i with hat on top space plus space straight j with hat on top close parentheses