How Far Will a 30 kg Cart Move in 3 Seconds with a 10 N Push?

[karush]

$\tiny{cp 3.6.11}$
$\textsf{A shopper in a supermarket pushes a loaded cart with a horizontal force of 10 N.}$
$\textsf{If the cart has a mass of 30 kg,}$
$\textit{a. how far will it move in 3s starting from rest }$
\begin{align*}\displaystyle
ma&=F \\
a&=\frac{F}{m} \\
&=\frac{10N}{30 \, kg} \\
&=.333 \, m/s^2\\
x&=x_o + v_o t+\frac{1}{2}at^2 \\
&=0+0+(.333 \, m/s^2) \cdot (3 s)^2 \\
&\approx \color{red}{3 \, m}
\end{align*}ok I think this is ok
but the notation could be better
so suggestions

 

[tkhunny]

Thought Questions:

1) Where did the 1/2 go?
2) Are you SURE the acceleration is constant?
3) No friction at all?