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

The angular frequency `omega` of the body
`omega = 2pi "rad./s"" ""Time period T" = (2pi)/(omega) = 1s`
At t = 1.5 s
(a) y = 5.0 (m) `cos (2pi xx 1.5 + pi//4)`
`= 5.0 (m) cos (3pi + (pi)/(4))`
`= -5.0 xx 0.707 =-3.535 m`
(b) Speed `(dy)/(dt) = -5.0 (m)`
`2pi sin (2pi xx 1.5 + pi//4)`
`=- 5 xx 2pi sin (3pi + pi//4)`
`= 10 pi xx 0.707 = 22.20 m//s`
(c) Acceleration of the body at t = 1.5 s
`a = -omega^(2) y" "-(2pi)^(2)(-3.535)`
`a = 1.39.56 m//s^(2)`