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I'm working on a homework problem in Mathematica. We have to graph the height and the velocity of a function given an initial height and initial velocity. However, when I do the graph for the velocity with an initial velocity of 0 and an initial height of 100, the entirety of the velocity part of the graph is negative. Shouldn't the velocity be increasing as the object falls?

That is the graph and functions I am using. I have a feeling either something is typed wrong that I have overlooked in my numerous attempts to find it, or that there's something I'm just not understanding about what the graph is actually telling me.

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2 Answers

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Velocity is a vector, in your case 1-dimensional, and so its sign indicates its direction. It is a matter of convention which direction is taken to be positive, but you can establish the convention in use by examining your formula

\begin{equation} h = - 16 \cdot t^2 + v \cdot t + h_0 \end{equation}

The first element on the right comes from acceleration, the second from initial velocity and the last is the initial height.

Now, consider how h changes for very small t, i.e. before the effect of acceleration becomes visible. As you can see positive v leads to h increasing with time, i.e. velocity oriented upward. Similarly, negative v leads to h decreasing with time, i.e. velocity oriented downward.

This means that your code is probably correct assuming it does not violate some externally defined velocity sign convention.

The way you read your graph is this: negative velocity means the body falling down, positive velocity means the body climbing. If you start with initial velocity zero, you would expect the body to start falling immediately, which is indeed what happens. If you set the initial velocity to a positive number, it will start positive, indicating that the body initially climbs, then it will linearly decrease to zero, indicating that it slows down until it stops at the highest point and finally the velocity will become negative indicating that the body starts to fall down.

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This makes a lot more sense now, thanks. I just wasn't understanding how to read the graph of velocity; I don't remember much from high school physics so I forgot about the vector bit. All seems to click now though. –  SnoringFrog Mar 6 '12 at 17:42
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speed = absolute value of velocity Speed is increasing. Think which way is positive on your vertical axis. If it's going that direction, the velocity will be positive. If it's going the opposite direction, the velocity will be negative.

Hope that helps.

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Took me a minute to figure out what you were saying, but I get it now. Thanks. –  SnoringFrog Mar 6 '12 at 17:40
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