Physics 1.06 Speed

Overview in the help site is our first variable to visit.

So, number one says, I can describe the variables and vocabulary needed to analyze speed and identify them on motion graphs.

Number two, I can compare and contrast average speed and instantaneous speed.

And then number three, I can calculate average speed using the proper equations and apply the three-step method and rubric, which we'll talk about in a moment.

So let's look at the equations first.

Remember, there is an equation sheet for 1st semester on the announcement page and in the Hope center.

We encourage you to either bookmark that or to print a copy.

And today's equations are average speed formula.

Speed is equal to the total distance divided by the time of the situation.

This will be the main focus of our lesson, and I would say a lot of students might remember an equation similar to this, from algebra class.

Instead of speed, the term was probably rate, but very similar idea here.

Now, there is an additional equation also taught within this lesson.

It's also considered an average speed formula, but it has some very specific conditions, and we're not quite ready to use this one as much as maybe the lesson is introducing.

So I'll go over this one briefly, but remember that this 1st equation will be your primary focus.

Um, and really the catch to the 2nd equation is that it can only be used during what we call uniform acceleration.

So this rabbit, here's a great example.

The rabbit might be starting with an initial speed of zero, not moving at all. And quickly accelerating, That process of speeding up can be used to figure out an average speed.

What we do is we add the initial speed, and the final speeds together, and divide by two.

It almost feels more like a mathematical average.

But the only time we can use this equation is if the object, or person or animal, has been speeding up during the process of their motion.

So we'll actually dig into this type of scenario much more as we get further into the course.

Um, we'll focus really on this 1st equation and kind of look at all the parts and pieces to analyzing that one.

So let's go on to do that.

As we talked about in one of our first.

As we talked about in one of our first lessons, we do have symbols or variables for the quantities that we talk about, and then, of course, that physical quantity name, and the typical units.

So, as you can see on the list here, we are focusing on speed, and in order to calculate a speed, we need to know how long this object is moving and how far.

So time and distance.

And of course, I think time and distance are pretty intuitive, right?

T is for distance, T is for time. Makes sense.

The one that might be a little confusing or questionable at 1st is average speed.

Why would it be a V?

And we'll talk about the application of V later.

But for now, we want to realize that V is the letter we should be using for average speed.

And the units are meters per second.

Time would be measured typically at seconds, distance in meters.

And then, like I mentioned earlier, initial and final speeds.

Or what would that, oh, there, could be standing for original.

So technically, the O and the FPR subscripts, and we would say the sub F, the sub O, per final speed, and original speed.

And we'll dig into those much more in upcoming lessons as well.

Now, a couple other terms that you want to make sure, you read through in the lesson, our kinematics, which shortly is the study of motion, is what we're going to spend a lot of first semester physics on.

And then relative motion, and there's a little activity within the lesson to do there.

I won't be talking about that in particular, in this recording, so make sure you definitely dig into that.

Okay, so the formatting on this page got a little wonky, but I think we can make it through.

Um, so, like I was saying, with our first objective.

We want to be able to use these terms to describe, and they're very connected to motion graphs as well.

So there's some things to know about motion graphs that will make this analysis easier.

So, we're going to be focusing on what we call a position versus time graph at first.

And the position's always going to be on your Y axis and time will always be on the X. So that, those are kind of standards to our model that will be analyzing.

And what you want to do is practice reading points on the graph and really visualize the context of the situation.

What's really happening to this object or animal or person?

One good reference is the Y intercept.

Whether it is at 00 or maybe somewhere above zero.

It represents the starting point of the situation.

So that's really a good place to begin your analysis and then think about what's happening after that.

Reading for detail is important when analyzing graphs.

So we don't really want to just skim and kind of generalize.

We really want to look at the points on the graph. And use them to be very specific.

Um, in our either calculation or in our summary of what's happening.

So here is a pretty long scenario.

It actually is much longer than a lot of the graphs we'll look at.

But it is a type of ocean graph that will analyze quite often.

Notice its position versus time.

Position is on the Y axis.

Time is on the X, and those will always be the case.

Now later in the course, it might not be a position.

It might be another variable.

So you really want to double check as soon as you look at a graph.

What kind of graph am I really working with here?

All of the ones in this first lesson will be positioned.

Okay, so, let's read the example.

This one says a sloth attempts to cross a four lane road.

Use the graph to identify variables and calculate speeds.

So what you want to picture, you may have seen on social media, different videos of sloths slowly trying to cross a road.

It's quite adorable if you haven't seen it.

Uh, it takes them some time, though.

So, as I was saying earlier, 00 represents the sloth, right at the beginning of the scenario, and the fact that, um, they are really hoping to make it to the other side of this 4 lane road.

So, segment A, if I were to just focus on that, is telling me five, 10 seconds later, the sloth has covered one meter.

So, kind of picture 10 seconds.

Doesn't feel like a whole lot of time, but if you're watching a sloth crawl, It is, it feels like a long time.

They covered one meter.

Then, from 10 seconds to 25 seconds, which would be 15 more seconds, they made it to the 4 meter mark.

So if we picture that road, they made it one meter, then 15 seconds later, now they're at the four meter mark.

Okay, and now, from 2nd from 25 on the stopwatch to 35, so for these 10 seconds, we're at 4 meters, we're still at 4 meters, we're still at 4 meters.

So, anytime you see a flat horizontal line on a position versus time graph, it's, honestly, the boringest basic thing that could happen.

Nothing's happening.

The sloth is probably distracted and taking a break.

So we can say there's no motion happening in segment C, then from D, or from 35 to 45, another 10 seconds.

We can assume there's motion again, because there is a slope.

So we can see, they traveled from 4 meters to 4 meter mark to the 5 meter mark, so they covered one more meter during that little portion. Of their journey.

Then, from the 452nd mark to the 62nd mark, they traveled from the 5 meter mark, two, it's like 9.5 .

So that tells me there that I have, and I can visually see it too, a pretty steep slope.

And in a moment, we'll be able to calculate some of these to really figure out, well, how fast was this loss going just during that stretch of the trip?

Okay, and then lastly, we're back to a case where now we're at the 62nd mark at 9.5 meters.

We're still at 9.5 .

We're still at 9 and a half .

We can maybe assume they've made it to the other side of the road, and now they're just kind of hanging out there.

We don't really have the context of the situation to know that, but we can conclude that 1st segment F, the sloth is no longer moving again.

So, a good kind of place to visually start is to notice anytime there's a slope, that the sloth or the object would be moving.

Anytime that slope is zero, or the segment is flat, we're in a kind of a holding pattern, that object is not moving, or in physics, we call that at rest, as a common phrase, we'll say.

So now that we've kind of acclimated ourselves to what's happening here, um, let's take a look at how we would find average speed.

If we think back to the equation, it's pretty straightforward.

We need to know how far the object traveled, that distance, and we know how much time it took.

And then we're just going to calculate using the average speed equation.

So let's try number one.

It says, how far did this law travel in the first 30 seconds of the journey?

So here's where you really have to be careful.

And I often suggest to kind of read more than once, to make sure your mind didn't play any tricks on you.

I know I easily will say a completely different number than what's in the question, and I'll end up doing a calculation that's not even being asked for.

So when I reread, I'll double check here, says, how far?

Did the sloth travel in the 1st 30 seconds of the journey?

How far is asking me for distance?

1st 30 seconds, I know, would be to the 32nd mark on my graph.

So really, because it's asking how far, I'm not even doing a calculation for this one.

I'm finding the time they're asking about.

Finding that point on the graph, and then going over to that Y access to determine where, in that process of crossing those lanes, did the sloth make it to?

And easily enough, we can say that that point they are at the 4 meter mark.

So I would answer 4.00 meters.

And that's it, no calculation needed there, because it was data I could pull straight from the graph.

Now, for number two, it says, What is the sauce's average speed during the first 45 seconds?

So now I'm looking at a different spot on my graph?

I'm gonna change colors here.

I want 45 seconds.

I'm gonna double check.

I'm reading a number, right?

And then I need to see, well, where are they now?

I know, and if I were to make my Gibbons list, T is equal to 45 seconds, because that's what the question was asking for.

And then my other given really has to come from my interpretation of the graph.

If I go across, I can see that is at the five meter mark.

So now I have the two variables I need.

And for a lot of us, if we're comfortable with this particular equation, we might be just doing this math in our head, and we can kind of calculate it straight out.

If you're not there yet, and if you're looking to practice that thought process that's talked about in the lesson, the next step would be to list what are we looking for?

Average speed.

And then it would be to show the equation you've selected.

Now, the easy part is what we only have really one main equation we're talking about in this lesson.

So, more than likely, it's vehicles D over T. Later in the course, you may have 20 different equations to choose from, and it will be your job to identify which equation applies to the situation you're given.

So that section or that step will be increasingly important as we move forward in the course.

So I've shown my Gibbons, I've shown my unknown.

I've shown the equation I'm using.

And then from there, it really might be math.

You potentially could have done in your head, but we do want to see the documentation of it, and that's really showing all steps of your work.

So here, I would do the is equal to D. 5.00.

My zeros are awful.

But they're legible, I guess.

And he.

And one question that commonly comes up is, should I write the units in my math and my substitution?

You can, if you would like to, but I also find some students get a little confused with the additional letters in the math.

So you might want to use a different color font, if you want to try that, or simply not include them till the end.

Your choice there.

And then, it's a matter of getting our calculator out and doing that math real quick.

So if you haven't already, go ahead and grab a calculator and do that division.

And often, we would possibly in math, maybe reduce this as a fraction.

In physics, we would not.

We would type this in, and a 1st step could be to just write what the calculator gives you.

I'm getting a whole bunch of ones repeating.

That doesn't have as much meaning as what we should do, which is rounding our final answer to the proper significant digits.

So based on what we're seeing here in the data given, we had three significant digits for the time.

And it looks like about 3 for the distance.

So I would keep 3 here.

And my answer would be point, one, one, meters per second.

And the reason I know the units are meters per second is from the chart we started with, of course, but also because, and I'm going to do a different font color here, just to distinguish it.

Um, the distance traveled was in meters.

The time that passed was in seconds, and we did division.

So mathematically, it makes sense that it should be meters per second.

Kind of a way to prove those units.

And that is the final answer.

Now, again, make sure, when you are showing your work, you're thorough in every step.

Also, you're not using outside resources.

And of course, using only the equations that are introduced within the lessons, also on the equation sheet.

All right, I'm going to erase all of that, and we just have a couple more things.

So, in core idea number two, we need to be able to distinguish, or compare and contrast, distinguish, average speed from instantaneous speed.

And I feel there's a good root word here, that really gives it away.

Instantaneous has the word instant in it.

So that's a good visual reminder of what we should be thinking about here.

Let's read these two scenarios and see how they match up.

The one says, Milo the Mouse and Cara the Chipmunk are cruising along.

When they spot Officer Whiskers, the cat parked on the roadside.

Oh, no, Kara whispers, glancing at the dashboard.

How fast are we going right now?

Number two.

Milo, the mouse, and Caro, the chipmunk, finally roll into Sunny Shore City.

Phew.

That was a long trip, says Milo.

We drove 180 miles and 3 hours.

How fast do you think we traveled for the whole journey?

So think about those two and one would be considered average speed.

The other would be considered instantaneous.

And I have a little chart here to visually compare those.

Anytime you're talking about right now, or that phrase, or that piece of those word, I guess the prefix, or the bass, something your English teachers would say, is the word instant.

So right now, this instant would be scenario one, Kara here is worried she might be getting a ticket, right?

Um, the overall time, we're looking at a span of time, we're really expecting to be calculating an average speed.

We're probably pretty certain they weren't going the exact same speed that entire time.

That would be very hard to do on really any given highway.

Um, so if it is a duration of time, you're more than likely finding an average speed.

So pretty straightforward there, but they are easy to kind of mix up.

So watch out for that.

And then, left.

Poor idea number three.

Here's where we are really looking at that rubric that's in the lesson.

And Miss Q and I will be using this to help score your essay questions.

You basically get one point for listing the Gibbons.

Are you able to interpret what the scenario is sharing, using the proper symbols, and also making any conversions?

And we'll see that in this example coming up.

Uh, point.

Also mention what you're really looking for, which would be the unknown.

That one, I think, is probably the most forgotten, honestly.

Um, point.

The next point comes for choosing that proper equation, and it needs to be shown in the course, not one you find in an outside resource.

The next point is really doing the work, showing that process, because really in physics, The final answer is important, but the way you got there is equally important.

So showing the substitution and the algebra.

Even if you're used to doing some of the math mentally.

We want to see what you're thinking.

So, kind of documenting that is the expectation.

And then lastly, the remaining points are for your solution.

What did all that work result in?

We're looking for, of course, that correct answer ideally, with proper significant digits and the correct units.

Also, um, I find, and honestly, I do this myself too.

I like working out a calculation on paper.

I feel like sometimes my brain just operates better when I do that.

You're welcome to do that, but remember once you've completed your calculation, you do need to type it.

We cannot accept images of written work.

And that's really a school policy.

So I would say have scrap paper around.

A lot of times it might be easier to write out your calculation. But realize you will have to also type it.

So hopefully that helps there.

And let's take a look at this one.

Um, it says, a student rides their bike from home to the park. Traveling 2.4 kilometers in 12 minutes.

What is the student's average speed in meters per second?

So here's one where the question is asking for units that are not in the gibbons.

That would indicate that you would need to show your conversion up at the beginning in that given part.

And here is a walkthrough of what to expect.

So here's the rubric, rubric, side by side with the work.

I know, uh, a lot of comments I get in the past have been, well, all I did was divide, and then I got the answer.

We understand that especially with his equation, it may just be multiplication or division, depending on what you're solving for, but we also need that documentation of any conversions that you can complete that you needed to complete.

And how you did those.

So here's the 1st one. Distance is 2.4 kilometers, but every kilometer is a 1000 meters.

So multiplying by 1000 was needed for this step, or moving that decimal 3 places to the right means the same thing.

And you could write that out.

The time is 12 minutes.

Well, there's 60 seconds in every minute.

So multiplying that, gives us the time and the units we needed.

And then remember to always show what you're looking for.

In this case, the question asked for average speed.

Equation, substitution.

And then again, the calculator's going to be generous.

It is often gonna give us too many digits.

So, at the end, you might be writing the same answer or typing the same answer again for your final answer, but you also need to go back to round, and then really confirm you have the proper units.

So technically, if you were to just share a final answer, you would get two points out of five, because we didn't see all of the work coming before it.

So, be cautious of that, and, um, showing each and every detail is really where, um, you can show a demonstration of your understanding.

And then you also have something to refer back to if a mistake was made so that you can more easily identify and troubleshoot.

And Ms. Q and I can do that as well.

So I hope that helps.

I think we have just a recap here remaining.

So make sure you're reading physics for detail.

I often read a question 3 times.

Make sure the units agree, convert if needed.

Practice reading the data from graphs and really kind of make a little story out of it that often makes it easier.

Practice that 3 step method of showing your work.

And I would say have the 104 significant digit notes handy if you feel like that is something that's still a little rusty for you.

Looking back at those notes is perfectly fine.

Our equations from the equation sheet.

And what to know for the quiz.

It is 8 multiple choice questions. Practicing that scale of reading the data from your graphs, from given graphs, and then to calculations, where basically you're demonstrating that same process I just got done demonstrating.

So again, this is your overview video.

Be sure to read the lesson completely.

Take notes as you choose.

If there are any live lessons you'd like to attend related to this lesson, definitely check the announcement page.

And then when you're ready, that assessment.

Show what you can do.

Definitely reach out at any point if you have any questions, and have a great dayOverview in the help site is our first variable to visit.