Intro to Motion Questions
Transcript
Motion Questions. Perhaps the largest category of word problems concerns moving things and
距离、速度或时间的相关量。这些都与一个非常公式有关，D等于RT。
有些人喜欢记住这是DRT方程。想想看，你知道，事情在地面上移动
地面是泥土做的。
这有助于一些人记住这个公式。所以在这个公式中，它和距离D有关，R是速率或 speed, and T which is time. Each one of these quantities has units, and 在你的计算中记录单位是很重要的。速率的单位决定了距离和时间的单位。
如果速率以英里每小时为单位，则距离必须以英里为单位，t必须以小时为单位。如果速率以米每秒为单位，则距离必须以米为单位，并且 时间必须以秒为单位。同样，如果你知道 distance and time, that determines the units for rate. The same length unit and time unit need to be used in the units of all three.
注意，对于距离，D等于RT已经被求解了。如果需要的话，我们可以解决速度或时间的问题。 如果我们把初始方程的两边都除以T，我们就得到了速率。所以速率等于距离除以时间。 Alternatively, go back to D equals RT. Divide both sides by rate, and what we get is T equals d over r.
时间等于距离除以速度。这已经解决了。 It's very important to be comfortable moving back and forth between any of those three forms. 让我们做一些简单的计算来练习。
暂停视频，然后我们来讨论这三个问题。 Okay. The first question: What is the speed of someone who covers 240 miles in six hours at a constant speed? Well, we're given distance, we're given time, and we're looking for rate. So we want the version that is solve per rate.
Rate equals D over T. Then we're just gonna divide the distance by the time. 240, well 24 divided by 6 is 4, so 240 divided by 6 has to be 40. And that would be 40 and then miles over hours that's miles per hour. 40 miles per hour is the answer. Second question, how far does someone moving at 8 meters per second move in 40 seconds.
我们在这里寻找距离。所以我们要求距离的形式，D等于RT，原始形式， 我们只是把速率乘以8米每秒乘以40秒。8乘以4等于32，所以8乘以40等于320。 米每秒乘以秒等于米。所以这应该是320米。
最后，第三个问题， how much time does it take to move 300 feet at a speed of 20 feet per second? Well here we're looking for time, we know the distance and we know the rate,. 所以我们需要时间的形式。时间等于距离大于速度。
现在我们要用这个距离除以这个速率，当然我们可以取消0。那就剩下30比2，也就是15。 That's the number, and of course the time unit is second. So, time has to be in seconds. 必须是15秒。每一个问题本身都太简单了，不可能成为一个完整的测试题， but these solutions demonstrate the fundamental skills you will need.
In other words, in any distance rate and time problem, you're going to have to typically be doing one of those calculations a few times. 好吧，现在我需要找到这个距离，好吧，现在我需要找到那个时间。所以你要把不同的费率和时间放在一起 doing these calculations multiple times to get through a larger test question. What if the units given in the prompt and the units for which the prompt asks are inconsistent?
So, you might be given two different units in the prompt, and you might be given one unit in the prompt, and then ask for another unit. 我们该怎么办？嗯，我们需要改变单位，我们使用单位转换，比如一小时等于60分钟，或者一英尺等于12英寸。 Those are two very standard unit conversions. Often the test will give you the conversions for 不是很常见的。
Any unit conversion can be written as an equation, but it can also be written as a fraction equal to one. 所以，我们可以说1等于1英尺加12英寸，或者1等于12英寸加1英尺。 You see, that's awfully useful. If we have something equal to one, that means we can always multiply or divide by that, and we don't change the fundamental values.
So, much in the same way, you can you could always multiply a fraction, say, by something like seven over seven. That doesn't change the value of the fraction because you're really multiplying by one. Much in the same way, you can take any quantity and multiply it by something like one foot over twelve inches, or twelve inches over one foot.
You could multiply by either of these, and it wouldn't change the value either, because this is also multiplying by one. So here's a question. Pause the video and then we'll talk about this. 地衣每年在石板上生长4厘米。每年4厘米，就是这个速度。
如果这个速度随着时间的推移保持不变，穿越30米需要多少年？ 所以我们在找时间，所以我们要解决时间问题。时间等于距离大于速度。 But we have to take care of the inconsistent units because we have a speed.
涉及生丁ters, but a distance in meters. And of course the question is nice enough to tell us that one meter equals 100 centimeters. So our rate is 4 centimeters per year. 我们的距离是30米。最简单的办法就是马上把距离改成厘米。
So we're just gonna multiply by 100. We're gonna multiply by 100 centimeters over 1 meter, cancel the meters. And we get 3000 centimeters. So that's the distance, and the distance and time are in the same unit. 时间等于距离除以速度。3000除以4。
3000 divided by four is 750, and the time unit is year. So this is 750 years. Here's another question. Pause the video and then we'll talk about this. A car moving at 72 kilometers per hour moves how many meters in one second?
So we're told that 1 kilometer equals a thousand meters. Well, we also have to change hours to seconds. 我们知道一小时就是60分钟，每分钟有60秒。所以60乘以60等于3600。 一小时等于3600秒。这实际上是一个很好的数字，只要记住，因为它 does show up often enough that It's good that you don't have to recalculate it, just to know that one hour is 3,600 seconds.
Okay, well, now we can say that 72 kilometers over hours, 72 kilometers would be 72,000 meters, and one hour as we just thaw, saw, is 3600 seconds. 所以真的，速度是72000米，超过3600秒。我们将取消一些零。 Now notice that 72 is just 2 times 36. So if 72 over 36 is 2, 720 over 36 has to be 20.
So 20 meters per second. So it moves 20 meters in one second. In summary. D等于RT是运动物体的基本方程。知道da，怎么解R或T的方程。
It's already solved for D. We wanna be able to solve it for each of the three variables. 当你插上电源时，要记下数字的单位。不要忽略单位。 If you pay attention to units, that will really help you. Unit conversions can be written as fractions equal to one.
We can multiply or divide by them. That's very convenient. 了解常用单位换算和变换单位，使问题中的所有单位一致
Read full transcript
这有助于一些人记住这个公式。所以在这个公式中，它和距离D有关，R是速率或 speed, and T which is time. Each one of these quantities has units, and 在你的计算中记录单位是很重要的。速率的单位决定了距离和时间的单位。
如果速率以英里每小时为单位，则距离必须以英里为单位，t必须以小时为单位。如果速率以米每秒为单位，则距离必须以米为单位，并且 时间必须以秒为单位。同样，如果你知道 distance and time, that determines the units for rate. The same length unit and time unit need to be used in the units of all three.
注意，对于距离，D等于RT已经被求解了。如果需要的话，我们可以解决速度或时间的问题。 如果我们把初始方程的两边都除以T，我们就得到了速率。所以速率等于距离除以时间。 Alternatively, go back to D equals RT. Divide both sides by rate, and what we get is T equals d over r.
时间等于距离除以速度。这已经解决了。 It's very important to be comfortable moving back and forth between any of those three forms. 让我们做一些简单的计算来练习。
暂停视频，然后我们来讨论这三个问题。 Okay. The first question: What is the speed of someone who covers 240 miles in six hours at a constant speed? Well, we're given distance, we're given time, and we're looking for rate. So we want the version that is solve per rate.
Rate equals D over T. Then we're just gonna divide the distance by the time. 240, well 24 divided by 6 is 4, so 240 divided by 6 has to be 40. And that would be 40 and then miles over hours that's miles per hour. 40 miles per hour is the answer. Second question, how far does someone moving at 8 meters per second move in 40 seconds.
我们在这里寻找距离。所以我们要求距离的形式，D等于RT，原始形式， 我们只是把速率乘以8米每秒乘以40秒。8乘以4等于32，所以8乘以40等于320。 米每秒乘以秒等于米。所以这应该是320米。
最后，第三个问题， how much time does it take to move 300 feet at a speed of 20 feet per second? Well here we're looking for time, we know the distance and we know the rate,. 所以我们需要时间的形式。时间等于距离大于速度。
现在我们要用这个距离除以这个速率，当然我们可以取消0。那就剩下30比2，也就是15。 That's the number, and of course the time unit is second. So, time has to be in seconds. 必须是15秒。每一个问题本身都太简单了，不可能成为一个完整的测试题， but these solutions demonstrate the fundamental skills you will need.
In other words, in any distance rate and time problem, you're going to have to typically be doing one of those calculations a few times. 好吧，现在我需要找到这个距离，好吧，现在我需要找到那个时间。所以你要把不同的费率和时间放在一起 doing these calculations multiple times to get through a larger test question. What if the units given in the prompt and the units for which the prompt asks are inconsistent?
So, you might be given two different units in the prompt, and you might be given one unit in the prompt, and then ask for another unit. 我们该怎么办？嗯，我们需要改变单位，我们使用单位转换，比如一小时等于60分钟，或者一英尺等于12英寸。 Those are two very standard unit conversions. Often the test will give you the conversions for 不是很常见的。
Any unit conversion can be written as an equation, but it can also be written as a fraction equal to one. 所以，我们可以说1等于1英尺加12英寸，或者1等于12英寸加1英尺。 You see, that's awfully useful. If we have something equal to one, that means we can always multiply or divide by that, and we don't change the fundamental values.
So, much in the same way, you can you could always multiply a fraction, say, by something like seven over seven. That doesn't change the value of the fraction because you're really multiplying by one. Much in the same way, you can take any quantity and multiply it by something like one foot over twelve inches, or twelve inches over one foot.
You could multiply by either of these, and it wouldn't change the value either, because this is also multiplying by one. So here's a question. Pause the video and then we'll talk about this. 地衣每年在石板上生长4厘米。每年4厘米，就是这个速度。
如果这个速度随着时间的推移保持不变，穿越30米需要多少年？ 所以我们在找时间，所以我们要解决时间问题。时间等于距离大于速度。 But we have to take care of the inconsistent units because we have a speed.
涉及生丁ters, but a distance in meters. And of course the question is nice enough to tell us that one meter equals 100 centimeters. So our rate is 4 centimeters per year. 我们的距离是30米。最简单的办法就是马上把距离改成厘米。
So we're just gonna multiply by 100. We're gonna multiply by 100 centimeters over 1 meter, cancel the meters. And we get 3000 centimeters. So that's the distance, and the distance and time are in the same unit. 时间等于距离除以速度。3000除以4。
3000 divided by four is 750, and the time unit is year. So this is 750 years. Here's another question. Pause the video and then we'll talk about this. A car moving at 72 kilometers per hour moves how many meters in one second?
So we're told that 1 kilometer equals a thousand meters. Well, we also have to change hours to seconds. 我们知道一小时就是60分钟，每分钟有60秒。所以60乘以60等于3600。 一小时等于3600秒。这实际上是一个很好的数字，只要记住，因为它 does show up often enough that It's good that you don't have to recalculate it, just to know that one hour is 3,600 seconds.
Okay, well, now we can say that 72 kilometers over hours, 72 kilometers would be 72,000 meters, and one hour as we just thaw, saw, is 3600 seconds. 所以真的，速度是72000米，超过3600秒。我们将取消一些零。 Now notice that 72 is just 2 times 36. So if 72 over 36 is 2, 720 over 36 has to be 20.
So 20 meters per second. So it moves 20 meters in one second. In summary. D等于RT是运动物体的基本方程。知道da，怎么解R或T的方程。
It's already solved for D. We wanna be able to solve it for each of the three variables. 当你插上电源时，要记下数字的单位。不要忽略单位。 If you pay attention to units, that will really help you. Unit conversions can be written as fractions equal to one.
We can multiply or divide by them. That's very convenient. 了解常用单位换算和变换单位，使问题中的所有单位一致
