Answer
$-\sqrt 2$ m/s,
$\sqrt 2$ m/s,
$\sqrt 2m/s^2$,
$\sqrt 2m/s^3$
Work Step by Step
Given the position equation $s(t)=2-2sin(t)$, we have:
1. velocity at $t=\pi/4$, $v(t)=s'(t)=-2cos(t)=-2cos(\pi/4)=-\sqrt 2$ m/s
2. speed at $t=\pi/4$, $|v(t)|=\sqrt 2$ m/s
3. acceleration at $t=\pi/4$, $a(t)=v'(t)=2sin(t)=2sin(\pi/4)=\sqrt 2m/s^2$
4. jerk at $t=\pi/4$, $j(t)=a'(t)=2cos(t)=2cos(\pi/4)=\sqrt 2m/s^3$
