Verified answer

You have to understand the relationship between location, speed, and acceleration.

Location is unchanging over time when speed is zero.

Speed is unchanging over time when acceleration is zero.

(I used the phrase "over time" to mean "with the passage of time", NOT "divided by".)

Such a graph (for each kind of observation) will be a straight line. (Remembering WHAT is being observed: the thing identified by the y-axis.)

To rephrase, those first two kinds of observations in a graphical way:

Location is changing regularly over time when speed is constant but not zero.

Speed is changing regularly over time when acceleration is constant but not zero.

These are still straight-line graphs, but slanted up or down.

Notice your second question is also the second observation I described above: acceleration.

Imagine the plot of something moving with a fixed speed. That's the first type of observation I described. If the speed is ALSO changing, and doing so in a regular way, then that's acceleration, and the position of the object is changing in a manner similar to "constant speed", but with the passage of time, that movement is increased (or decreased) in every unit of time; it's like the line's movement is exaggerated, and the graph becomes curved. I'd like to say, the line moves upward even more so as you look to the right, but that's only true for positive acceleration, when acceleration adds to speed. We're talking now about a curve upward. But, if the acceleration is negative, the line that started upward (with positive speed), now regularly curves downward, because the speed is decreased by its negative acceleration.

Now, suppose the object starts with negative speed (moving away from a target). What would be a straight-line motion of location with respect to time, is now curved by acceleration, and the direction of curvature depends on whether the acceleration is positive or negative. Adding positive acceleration to negative speed, cause reversal of speed; adding negative acceleration to negative speed, causes a regular increase in speed, but downward.

These last two paragraphs above describe the look of plotted distance vs time for acceleration.

Graphing these things means the observed behavior would be represented by the y-axis, and time by the x-axis. The curves are called hyperbolas, and whether you see the point where they change direction in your graph depends on whether the acceleration starts off adding to or subtracting from the direction of the initial speed. Hyperbolas are the graphs for "second order" or quadratic functions. If location vs time is expressed as a function of time, squared, that is also a way of identifying the curve called a hyperbola. If you've ever seen the graph of movement due to gravity, it is a parabola. (Movement can start off either upward, downward, or stationary - like just before being dropped.)

Hey there!

I"m sorry to say that I'm not completely sure of the first problem... maybe the acceleration varies due to different distances and time.

But the second one means that since it is a straight line, whatever the line represents is constant.

Hope i helped some!

Lauren :]