$textbf{a.)}$ To get an initial velocity $v_0$, substitute $t=0$ into the velocity-time equation given in the task:

$$
v_f(0)=v_0=1-0.5cdot0
$$

$$
boxed{v_0=1:frac{text{m}}{text{s}}}
$$

$textbf{b.)}$ Refer to the standard form of the velocity equation. The cart’s acceleration is equal to the term with $t$:
$$v_f=v_0+at=1-0.5t$$
$$boxed{a=-0.5:frac{text{m}}{text{stextsuperscript{2}}}}$$

$textbf{a.)}$ $v_0=1: frac{text{m}}{text{s}}$\
$textbf{b.)}$ $a=-0.5:frac{text{m}}{text{stextsuperscript{2}}}$

$$
textbf{Concept :}
$$

We will calculate the velocity of eagle with velocity-time equation for constant acceleration.

$$
textbf{Solution :}
$$

Plug-in the numerical values in the equation we get

$$
v_f=v_i+a_{av}Delta t=(5.0m/s)+(1.3m/s^2)(2.0s)=color{#4257b2} boxed{bf 7.6m/s}
$$

$$
v_f= 7.6m/s
$$

In this problem, we are given the time varying velocity of three object.
begin{center}
begin{tabular}{|c|c|}
hline
Object & Velocity \ hline
1 & $2~mathrm{m/s} + left( 3~mathrm{m/s^{2}} right)t$ \ hline
2 & $-8~mathrm{m/s} – left( 4~mathrm{m/s^{2}} right)t$ \ hline
3 & $1~mathrm{m/s} – left( 5~mathrm{m/s^{2}} right)t$ \ hline
end{tabular}
end{center}
We compare their velocities and speeds at time $t = 3~mathrm{s}$, and rank them in increasing order.

Part A.

For the given time, we have
begin{center}
begin{tabular}{|c|c|c|}
hline
Object & Velocity & \ hline
1 & $2~mathrm{m/s} + left( 3~mathrm{m/s^{2}} right) left( 3~mathrm{m/s} right)$ & $v_text{1} = 11~mathrm{m/s}$ \ hline
2 & $-8~mathrm{m/s} – left( 4~mathrm{m/s^{2}} right) left( 3~mathrm{m/s} right)$ & $v_text{2} = -20~mathrm{m/s}$ \ hline
3 & $1~mathrm{m/s} – left( 5~mathrm{m/s^{2}} right) left( 3~mathrm{m/s} right)$ & $v_text{3} = -14~mathrm{m/s}$\ hline
end{tabular}
end{center}
We see that $$boxed{ v_{2} < v_{3} < v_{1} }$$

Part B.

The speed is the absolute value of the velocity. Let $s$ denote speed.
begin{center}
begin{tabular}{|c|c|}
hline
Velocity & Speed\ hline
$v_text{1} = 11~mathrm{m/s}$ & $s_{1} = 11~mathrm{m/s}$\ hline
$v_text{2} = -20~mathrm{m/s}$ & $s_{2} = 20~mathrm{m/s}$ \ hline
$v_text{3} = -14~mathrm{m/s}$ & $s_{3} = 14~mathrm{m/s}$\ hline
end{tabular}
end{center}
We see that $$boxed{ s_{1} < s_{3} < s_{2} }$$

begin{enumerate}
item [a)] $v_{2} < v_{3} < v_{1}$
item [b)] $s_{1} < s_{3} < s_{2}$
end{enumerate}