A particle moves according to a law of motion s=f(t) t ⩾0, where t is measured in seconds and s

step 1 All right, so here we're going to look at a object moving with a motion graph or position graph

A particle moves according to a law of motion s=f(t) t ⩾0,...

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? $f(t)=t^{3}-8 t^{2}+24 t$

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?
$f(t)=t^{3}-8 t^{2}+24 t$

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