A particle of mass m initially at rest is acted upon by a unidirectional force ` F=F_@cos ((pi)/(2) t) .` The distance travelled by the particle when it stops first in the subsequent motion is ,

Options

A. ` ( 2F_0)/( mpi ) `
B. ` ( 4F_0)/( pi^(2) m) `
C. ` ( 8F_0)/( mpi^(2))`
D. ` ( 2F_0)/(pi^(2) m) `

Answer

C

Explanation

` (dv)/(dt) =(F_0)/(m) cos ""(pit)/(2) rArr int _0 ^(v) dv = (F_0)/(m) int_0^(t) cos ""( pit)/(2) dt rArr v= ( 2F_0)/(pim ) sin ""(pit)/(2) `
`rArr `Distance traveled from t= 0 to t = 2sec . ` = int _0 ^(2) vdt `
= shaded area `=(2F_0)(pim ) int _0^(2) sin (pit)/(2) dt =(8F_0)/(pi^(2) m) `
` (##VMC_PHY_XI_WOR_BOK_01_C02_E03_031_S01.png" width="80%">