If the displacement of a body is given by ` x = 3 cos [ 2 pi t + pi/4]` m, then the acceleration of the body at t=2s is

Options

A. 0
B. `-6 sqrt2 pi^2 m//s^2`
C. `-10 pi^2 m//s^2`
D. `-12 sqrt2 pi^2 m//s^2`

Answer

B

Explanation

Displacement of a body is given by
` x = 3 cos [ 2pi t + pi/4 ] m `
velocity of body is given by `v = (dx)/(dt) `
` = (d)/(dt) [ 3 cos (2pi t + pi/4 ] )`
` =- 3 sin (2pi t + pi/4 ) . (2pi)`
` v = -6 pi sin (2 pi t + pi/4)`
Acceleration of body is given by ` a = (dv)/(dt)`
` = (d)/(dt) [ - 6 pi sin (2 pi t + pi/4) ]`
` = - 6pi cos (2pit + pi/4) .( 2pi)`
` a = 0 12 pi^2 cos (2 pi t + pi/4 ) `
at , t = 2s
` a = - 12 pi^2 cos ( 4pi + pi/4)`
` = -12 pi^2 cos pi/4 = - 12pi^2 . (1)/(sqrt2) `
` = - 6 sqrt(2) pi^2 m//s^2`