Answer
- Velocity $=-\sqrt2(m/s)$.
- Speed $=\sqrt2(m/s)$.
- Acceleration $=\sqrt2(m/s^2)$
- Jerk $=\sqrt2(m/s^3)$
Work Step by Step
$$s=f(t)=2-2\sin t$$
a) Velocity $v$:
$$v(t)=f'(t)=(2-2\sin t)'=0-2\cos t=-2\cos t$$
So, $$v(\pi/4)=-2\cos(\pi/4)=-2\times\frac{\sqrt2}{2}=-\sqrt2(m/s)$$
b) Speed:
The speed at time $t=\pi/4$ $=|v(\pi/4)|=\sqrt2(m/s)$.
c) Acceleration $a$:
$$a(t)=v'(t)=(-2\cos t)'=-2(-\sin t)=2\sin t$$
So, $$a(\pi/4)=2\sin(\pi/4)=2\times\frac{\sqrt2}{2}=\sqrt2(m/s^2)$$
d) Jerk $j$:
$$j(t)=a'(t)=(2\sin t)'=2\cos t$$
Therefore, $$j(\pi/4)=2\cos(\pi/4)=2\times\frac{\sqrt2}{2}=\sqrt2(m/s^3)$$
