$A$ body oscillates with $SHM$ according to the equation (in $SI$ units):
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.

(N/A) The given equation is $x = 5 \cos (2 \pi t + \pi / 4)$. The angular frequency $\omega = 2 \pi \, rad/s$.
$(a)$ Displacement at $t = 1.5 \, s$:
$x = 5 \cos (2 \pi \times 1.5 + \pi / 4) = 5 \cos (3 \pi + \pi / 4) = 5 \cos (5 \pi / 4) = 5 \times (-1 / \sqrt{2}) \approx -3.535 \, m$.
$(b)$ Speed $v = dx/dt = -5 \times 2 \pi \sin (2 \pi t + \pi / 4)$:
At $t = 1.5 \, s$,$v = -10 \pi \sin (3 \pi + \pi / 4) = -10 \pi \times (-1 / \sqrt{2}) = 10 \pi / \sqrt{2} \approx 22.21 \, m/s$.
$(c)$ Acceleration $a = -\omega^2 x$:
$a = -(2 \pi)^2 \times (-3.535) = 4 \pi^2 \times 3.535 \approx 39.48 \times 3.535 \approx 139.56 \, m/s^2$.