yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Interpreting direction of motion from position-time graph | AP Calculus AB | Khan Academy


2m read
·Nov 11, 2024

An object is moving along a line. The following graph gives the object's position relative to its starting point over time. For each point on the graph, is the object moving forward, backward, or neither? So pause this video and try to figure that out.

All right, so we see we have position in meters versus time. So for example, this point right over here tells us that after one second, we are four meters ahead of our starting point. Or for example, this point right over here says that after four seconds, we are almost— it seems almost— four meters behind our starting point.

So let's look at each of these points and think about whether we're moving forward, backward, or neither. So at this point right over here, at that moment, we're about two and a half meters in front of our starting point. We're at a positive position of two and a half meters.

But as time goes on, we are moving backwards, closer and closer to the starting point. So this is— we are moving backward. One way to think about it, at this time, we're two and a half meters. If you go forward about half a second, we are then back at our starting point, so we have to go backwards.

And if we look at this point right over here, it looks like we were going backwards this entire time, while our curve is downward sloping. But at this point right over here, when we are about— it looks like five meters behind our starting point— we start going forward again.

But right at that moment, we are going neither forward nor backwards. It's right at that moment where we just finished going backwards, and we're about to go forward. And one way to think about it is, what would be the slope of the tangent line at that point? The slope of the tangent line at that point would be horizontal; and so this is neither.

So we can use that same technique to think about this point. The slope is positive, and we see that. All right, right at that moment, it looks like we are at the starting point. But if you fast forward even a few— even a fraction of a second— we are now in front of our starting point. So we are moving forward.

We are moving forward right over here, and at this point we are at our starting point. But if we think about what's going to happen a moment later, a moment later, we're going to be a little bit behind our starting point. And so here we are moving backwards.

And we're done.

More Articles

View All
Inventing Graphics on Cave Walls | Origins: The Journey of Humankind
Early humans communicated with pictures and markings painted on cave walls and began to gradually work out symbols. As these markings spread and were understood and accepted, then you had the widespread transmission of ideas. We can see the very early day…
Impact of the Crusades
We’ve already had several videos where we give an overview of the Crusades. Just as a review, they happen over roughly 200 years during the High Middle Ages. The First Crusade, at the very end of the 11th century, was actually the most successful of the C…
Walking Alone in the Wilderness: A Story of Survival (Part 2) | Nat Geo Live
Why I’m here today, talking to you, here, in this amazing special place? It’s because of a slug story. Basic slug story, you know how those stories go? You know, I couldn’t have my pocket money when I was a kid. Grow up in Switzerland. Picture this. This …
LEVELS of INCOME (Explained)
People like to look at income from a narrow perspective: lower class, less than you make; middle class, however much your current salary is; upper class, substantially more than you make. But having started at the bottom and crawling our way toward the to…
How This Prawn Can Kill You - Allergies Explained
If you’re a fan of our work, you probably value rigor and humility in research and are willing to change your mind based on new information. You might also appreciate the same principles applied to important questions like: how can my donation make the bi…
Rhinoplasty Confusion (Clip) | To Catch a Smuggler | National Geographic
What were you doing in Mexico? Oh, okay. A couple of people have been doing that. Here’s an essential part of entry with the summer upon us. We have high traffic, a lot of crossers. So we’re seeing an increase of narcotics smuggling, people smuggling. CO…