A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude…

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F=F01-t-TT2 where F0 and T are constants. The force acts only for the time interval 2 T. The velocity v of the particle after time 2 T is:
  1. 2 F0 TM
  2. F0 T2M
  3. 4 F0 T3M
  4. F0 T3M

Solution

t=0, u=0

a=FoM-FoMT2(t-T)2=dvdt

∫0vdv=∫t=02 TFoM-FoMT2(t-T)2dt

V=FoMto2 T-FoMT2t33-t2 T+T2t02 T

V=4 FoT3M

Asked in: JEE Main 2021 (27 Jul Shift 2)

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