Answer
(a) $v(t) = 8~cos~t$
$a(t) = -8~sin~t$
(b) $x(t) = 6.93~cm$
$v(t) = -4~cm/s$
$a(t) = -6.93~cm/s^2$
The mass is moving to the left at that time.
Work Step by Step
(a) $x(t) = 8~sin~t$
$v(t) = x'(t) = 8~cos~t$
$a(t) = v'(t) = -8~sin~t$
(b) $x(t) = 8~sin~\frac{2\pi}{3} = 6.93~cm$
$v(t) = 8~cos~\frac{2\pi}{3} = -4~cm/s$
$a(t) = -8~sin~\frac{2\pi}{3} = -6.93~cm/s^2$
Since the velocity is negative, the mass is moving to the left at that time.
