The motion of a particle of mass m is given by x = 0 for t lt 0 s, x(t) = A sin 4pit for 0 lt t lt (1/4) s (A gt 0) andx =0 for t gt(1/4) s whichof the following statements is true ?

The motion of a particle of mass m is given by x = 0 for t lt 0 s, x(t

1.	The motion of a particle of mass m is given by x = 0 for t lt 0 s, x(t) = A sin 4pit for 0 lt t lt (1/4) s (A gt 0) andx =0 for t gt(1/4) s whichof the following statements is true ?
Answer» The force at `t=(1/8)` on the particle is `-16 pi^(2)A-m` The particle is acted UPON by on impulse of magnitude `4pi^(2)` A - m at t = 0 s and `t=(1/4)s` The particle is not acted upon by any force The particle is not acted upon by a constant force Solution :(A,B,D ) x= 0for `tle0 ` sec for0 `ltt lt (1)/(4)s` `v= (dx )/(dt )= 4 piA cos ( 4pit ) ` Att = `(1)/( 8)` sec `=-16 pi^(2)A SIN ((pi)/( 2))` Nowforce F = ma (t ) `=m[-16 pi^(2) A]` `=-16 pi^(2)Am` Now impulseof force CHANGEIN mometum `=(-16pi^(2) mA sin pi ) ^(1/4) = 0` Theimpulsechangein linearmomentuma `t=0` issameas at`t= (1)/(4) ` sec