A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pirads^(-1))t+pi//4]`
At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body.

Explanation

`omega = 2pi rad//s, T = 2pi//omega = 1s`
t = 1.5 s
(a) Displacement of the body at t = 1.5 s will be
`x = 5 cos [2pi xx 1.5 + pi//4] = 5 cos (3pi + pi//4)`
` = -5 cos pi//4 = (-5)/(1.414) = -3.535` m
(b) Velocity of the body at t = 1.5 s will be
`v = (dx)/(dt) = (d)/(dt) [5.0 cos (2pit + pi//4]`
` = -5.0 xx 2pi sin (2pit + pi//4)`
` = -5.0 xx 2pi sin(2pi xx 1.5 + pi//4)`
` = -5.0 xx 2pi sin (3pi + pi//4)`
` = + 5.0 xx 2pi sin pi//4 = (5.0 xx 2 xx 3.14)/(1.414)`
=22.2 m/s
(c ) ` a = (dv)/(dt) = (d)/(dt) [=10pi sin (2pit + pi//4)]`
` = -20pi^(2) cos(2pit + pi//4)`
` = -4pi^(2) [5.0 cos (2pi + 1.5 + pi//4)]`
` = -4 xx 9.87 xx (-3.535)`
` = 139.56 m//s^(2) = 140 m//s^(2)`