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

AI Thread Summary
A shopper pushes a 30 kg cart with a force of 10 N, resulting in an acceleration of 0.333 m/s². Using the kinematic equation, the cart will move approximately 3 meters in 3 seconds from rest. The discussion raises questions about the notation used, the assumption of constant acceleration, and the neglect of friction. Clarifications on these points could improve the analysis. Overall, the calculations indicate a straightforward application of Newton's second law and kinematics.
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$\tiny{cp 3.6.11}$
$\textsf{A shopper in a supermarket pushes a loaded cart with a horizontal force of 10 N.}$
$\textsf{If the cart has a mass of 30 kg,}$
$\textit{a. how far will it move in 3s starting from rest }$
\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
 
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Thought Questions:

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