Answer
$0$ m/s,
$0$ m/s,
$-\sqrt 2m/s^2$,
$0m/s^3$
Work Step by Step
Given the position equation $s(t)=sin(t)+cos(t)$, we have:
1. velocity at $t=\pi/4$, $v(t)=s'(t)=cos(t)-sin(t)=cos(\pi/4)-sin(\pi/4)=0$ m/s
2. speed at $t=\pi/4$, $|v(t)|=0$ m/s
3. acceleration at $t=\pi/4$, $a(t)=v'(t)=-sin(t)-cos(t)=-sin(\pi/4)-cos(\pi/4)=-\sqrt 2m/s^2$
4. jerk at $t=\pi/4$, $j(t)=a'(t)=-cos(t)+sin(t)=-cos(\pi/4)+sin(\pi/4)=0m/s^3$
