#### Problem 3E

$1-4$ A particle moves according to a law of motion $s=f(t)$, $t \geqslant 0$, where $t$ is measured in seconds and $s$ in feet.

(a) Find the velocity at time $t$.

(b) What is the velocity after 1 second?

(c) When is the particle at rest?

(d) When is the particle moving in the positive direction?

(e) Find the total distance traveled during the first 6 seconds.

(f) Draw a diagram like Figure 2 to illustrate the motion of the particle.

(g) Find the acceleration at time $t$ and after 1 second.

(h) Graph the position, velocity, and acceleration functions for $0 \leqslant t \leqslant 6$

(i) When is the particle speeding up? When is it slowing down?

3. $f(t)=\sin (\pi t / 2)$