Hey

mathlearn!

Here's what the acceleration and speed graphs would look like (using our new TikZ drawing capabilities

):

\begin{tikzpicture}[ultra thick]

\draw[red] (0,5) node[above] {\Large $a$} -- (5,5) -- (5,0) -- (10,0);

\draw[blue] (0,0) node[above] {\Large $v$} -- (5,3) -- (10,3);

\end{tikzpicture}

On the inclined plane we have a constant acceleration, and when it ends, the acceleration becomes near zero.

As a result the speed increases linearly until the end of the slope, after which the speed remains constant (although in reality it would linearly decrease slowly until zero).

Note that $v=\int_0^t a\,dt$.

However, we're asked for the displacement, which we can call $d$.

We have that $d=\int_0^t v\,dt$.

What would the displacement graph look like?