### BBC Bitesize - GCSE Combined Science - Describing motion - AQA - Revision 1

Your acceleration is meters per second2, and your final speed is meters per second. Now find the total distance traveled. Got you, huh? “Not at all, ”. Hi, I am having trouble understanding the relationship between speed, distance and time. For example, if time was tripled, what would be the. relationships between speed and distance and between duration and distance integrate these relationships spontaneously and thereby recognize problems.

- Thinking distance
- Displacement, velocity, and time
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The X value should be whatever time it took for the car to reach the end of your test course, your Y value is the distance you had the car travel 1. Using your ruler and pencil, connect the two points to make a line. Now, plot the velocity of the faster car. Your first point should be at 0,0 cm because this car will not get a head start. Your second point for the fast car is the velocity you measured. Using your ruler and pencil connect the two points to make another line.

Make this line look different than the first, either by making dashes or making it darker.

Label the lines fast car and slow car. Find where the two lines cross. At this intersection point, trace one line to X axis, and another to the Y axis. These are the lines with arrows on diagram 1. The two values you see are the time and distance where the fast car should overtake the slower car. Mark the predicting passing point on your course. Mark off the calculated point where the faster car should overtake the slower car.

Have your assistant release the slower car at the head start mark while you simultaneously release your faster car at the starting line. Start the timer a third person might be nice for this. Watch carefully to see where the fast car overtakes the slow car. Compare your predicted time and distance that the fast car overtook the slower car with the actual values.

Results Your results are likely to be pretty close to what your graph predicts, but they will likely vary depending on the velocities of your cars and whether or not they travel at a consistent velocity. Conduct more trials if you wish. Uniform velocity is a linear function, making them easy and fun to predict. Although the slower car had a head start in distance, the faster car covered more distance in less time, so it caught up. This is where the lines crossed. You should always say, hey, that's just manipulating one of those other formulas that I got before.

And even these formulas are, hopefully, reasonably common sense. And so you can start from very common sense things-- rate is distance divided by time-- and then just manipulate it to get other hopefully common sense things. So we could have done it here. So we could have multiplied both sides by time before we even put in the variables, and you would have gotten-- So if you multiplied both sides by time here, you would have got, on the right hand side, distance is equal to time times rate, or rate times time.

And this is one of-- you'll often see this as kind of the formula for rate, or the formula for motion. So if we flip it around, you get distance is equal to rate times time. So these are all saying the same things. And then if you wanted to solve for time, you could divide both sides by rate, and you get distance divided by rate is equal to time.

## The relationship between Distance, Speed and Time

And that's exactly what we got. Distance divided by rate was equal to time. So if your distance is meters, your rate is 3 meters per second, meters divided by 3 meters per second will also give you a time of seconds. If we wanted to do the exact same thing, but the vector version of it, just the notation will look a little bit different.

And we want to keep track of the actual direction. So we could say we know that velocity-- and it is a vector quantity, so I put a little arrow on top.

Velocity is the same thing as displacement. Let me pick a nice color for displacement-- blue.

### Relationship between distance traveled and speed - Maple Programming Help

As displacement-- Now, remember, we use s for displacement. We don't want to use d because when you start doing calculus, especially vector calculus-- well, any type of calculus-- you use d for the derivative operator. If you don't know what that is, don't worry about it right now.

But this right here, s is displacement. At least this is convention. You could kind of use anything, but this is what most people use. So if you don't want to get confused, or if you don't want to be confused when they use s, it's good to practice with it. So it's the displacement per time. So it's displacement divided by time. Sometimes, once again, you'll have displacement per change in time, which is really a little bit more correct.

But I'll just go with the time right here because this is the convention that you see, at least in most beginning physics books.

So once again, if we want to solve for time, you can multiply both sides by time. And you get-- this cancels out-- and I'll flip this around. Well, actually, I'll leave it like this. So you get displacement is equal to-- I can flip these around-- velocity times change in time, I should say. Or we could just say time just to keep things simple.

### Energy and Distance

And if you want to solve for time, you divide both sides by velocity. And then that gives you time is equal to displacement divided by velocity. And so we can apply that to this right over here.

Our displacement is meters to the east. So in this case, our time is equal to meters to the east. Well, they give us the velocity of 3 meters per second per the east. And once again, divided by 3 will give you And then when you take meters in the numerator, and you divide by meters per second in the denominator, that's the same thing as multiplying by seconds per meter, those cancel out. And you are just left with seconds here. One note I want to give you. In the last few problems, I've been making vector quantities by saying to the east, or going north.

And what you're going to see as we go into more complex problems-- and this is what you might see in typical physics classes, or typical books, is that you define a convention. That maybe you'll say, the positive direction, especially when we're just dealing with one dimension, whether you can either go forward or backwards, or left or right.

We'll talk about other vector quantities when we can move in two or three dimensions. But they might take some convention, like positive means maybe you're moving to the east, and maybe negative means you're moving to the west. And so that way-- well, in the future, we'll see, the math will produce the results that we see a little bit better. So this would just be a positive meters.

This would be a positive 3 meters per second. And that implicitly tells us that that's the east. If it was negative, it would then be to the west. Something to think about. We're going to start exploring that a little bit more in future videos.

And maybe we might say positive is up, negative is down, or who knows. There's different ways to define it when you're dealing in one dimension.