![]() Rate at 5 meters per second, but let's say that Let's say that our rate is, let's say, let's keep our When you do the dimensional analysis, it makes sure that the It's useful for something as simple as distance equals rate times time, but as you go into physicsĪnd chemistry and engineering, you'll see much, much, much more, I would say, hairy formulas. That's cute and everything, "but this seems like a littleīit of too much overhead "to worry about when I'm just doing "a simple formula like this." But what I want to show you is that even with a simple formula like distance is equal to rate times time, what I just did couldĪctually be quite useful, and this thing that I'mĭoing is actually called dimensional analysis. Our end units for distance were in meters, which Out like algebraic objects, they worked out so that We would be left with 50, and the units that we're Those are going to cancel out, and 5 times 10, of course, is, 5 times 10, of course, is 50. Seconds in the denominator multiplied by seconds in the numerator. If we were to treat our units as these algebraic objects, we could say, hey, look, we have seconds divided by seconds, or you're going to have This is the same thing as 5 times 10, 5 times 10 times meters per second, times meters per second times seconds, times seconds. What's neat here is weĬan treat the units, as I've just said, likeĪlgebraic constructs, kind of like variables, so this would be equal to, well, multiplication, it doesn't matter what order we multiply in, so we can change the order. Is equal to our rate, 5 meters per second times our time, times our time, which is 10 seconds. Pretty straightforward way, apply this formula. Were to give you a rate, if they were to say a rate of, let's say, 5 meters per second, and they were to give you a time, a time of 10 seconds, then we can pretty, in a Getting the results in units that actually make sense. What I want to do in this video is use this fairly simpleįormula right over here, this fairly simple equation, to understand that unitsĬan really be viewed as algebraic objects, that you can treat them like variables as we work through aįormula or an equation, which could be really, really helpful to make sure that we're Multiple times in our life that distance can be ![]() You are left with the meter on RHS which is the same unit on LHS, this is the basis of DIMENSIONAL (Using Dimensions) ANALYSIS (I don't have to give the meaning do I?) or DAġ hour has 3600 seconds(Ok mind is steady)ġhr(given in question) * 3600 s/1hr (read as 3600seconds per hour, logically that is correct right?) The s in the denominator(speed) and s in the numerator(seconds) cancel out. If you have understood till here then you can try using DA to find 18000m in km. Now calc the numbers and the units of hours cancel out leaving 3600 seconds.ĥ m / s * 3600 s The seconds Unit cancels.You are left with 18000m. If you are pretty fast your mind will think of converting time to sġ hour has 3600 seconds( Ok mind is steady)ġhr(given in question) * 3600 s/1hr ( read as 3600seconds per hour, logically that is correct right?) ![]() ![]() You are left with the meter on RHS which is the same unit on LHS, this is the basis of DIMENSIONAL (Using Dimensions) ANALYSIS ( I don't have to give the meaning do I?) or DA ![]() What is the distance I have traveled?Ģ0*20=> 400 (That seems so simple isn't it?) Let's say I am going at 20 m/s speed in 20 seconds. The quantity in the bracket is their unit There is nothing much to worry We know distance = Speed * Time ![]()
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