The speed of light is approximately 3.00×10 8 m/s. Convert this speed to yards/week (yd/wk).

Hey, guys. Let's check out this practice problem. We're gonna convert the speed of light which is 3 times 10 to the 8th, and this is in meters per second. And we want eventually, we wanna convert the speed to yards per week. Kinda strange, but we're gonna follow the steps of our unit conversions. So let's just get right to it. So we're gonna start off with our given target and, sorry, our given number and our unit, which is 3.00 times 10 to the 8th. And our units are in meters per second. Now I'm gonna have to multiply by some conversion factors in order to eventually get to yards per week. So what I like to do, especially when I have multiple units that I'm gonna have to convert, notice how meters per second is different from yards per week, is I wanna start with the top one. So let's start off with by just basically trying to handle the top unit and get it to yards. So what I wanna do is multiply by some conversion factors expressed as fractions. So if I look at my table here of my conversion factors, and by the way, this isn't all of them, this is just some of them might be helpful. 1, the one that I have here is meters to feet. So this is basically a conversion from metric to imperial. So what I wanna do is I wanna express this as a fraction, but remember we want opposite sides to cancel, units on top versus units on bottom. So I want meters to be on the bottom so that it cancels, and then eventually, this conversion factor is 0.305 and then 1 feet. So now I've got feet, but I'm not quite done yet because remember, I'm left with feet but eventually, I wanna make it to yards. So I have another conversion factor over here. And one conversion factor you might wanna know is that 1 yard is equal to 3 feet in the imperial system. So this is something that isn't in this table, but it's something that that is pretty common knowledge. 1 yard is 3 foot. So we've got feet and we wanna cancel out the units of feet, top and bottom. So now I want the conversion factors that feet are on the bottom and they cancel like this. So I've got 3 feet on the bottom and then 1 yard at the top. So now once I do this, basically I'm left with just yards on the top. So I'm done with the top unit, and I don't have to do anything else. Now what I wanna do is I wanna handle this bottom unit which is seconds because eventually, I wanna get it to week. So I have another conversion factor that I'm gonna stack on here. And now what I wanna do is I wanna cancel out seconds and I wanna get to weeks. So one thing we know is that there are 36 100 seconds in 1 hour. So that's one way we can go. Basically, we just have to do a bunch of time conversions to get up to a week. So we've got 36 100 seconds per 1 hour. So that will cancel out seconds with seconds. And then we've got another one because we're not done yet. So you have to keep going. Well, if we want to get to to weeks, we have to go even bigger. But again, we're still not done yet because we're in days. Now if 1 a week, then that's just going to be 7 days per week. Right? So there's 7 days in 1 week. And eventually, days will cancel with days. And now we're finally left with weeks. So notice how we eventually have ended up at our target units, yards on the top and weeks on the bottom. So now what we have to do is we have to multiply everything that's here on the top and then we have to divide by the multiplication of everything that's here on the bottom. Basically, what you're gonna do is you're gonna do 3 times 10 to the 8th times and you can ignore all the ones. We're gonna have to do times 36100. And I'm just talking about the numbers here because we've already made sure that the units will cancel. Times 24 times 7. So that's everything that's on the top. And multiply this in parentheses in your calculator. Then what you wanna do is you wanna divide by in parentheses, everything that's on the bottom multiplied. So we want, 0.305 times, and then we've got 3 over here. So that's basically all of your non one numbers. The numbers that aren't one in your top and bottom, you multiply them all and then divide them at the end. Use a parenthesis in your calculator, and what you're gonna end up with is you're gonna end up with 1.98 times 10 to the 14th in yards per week. That's how you handle the speed conversions and that is our answer. So if we look at our answer choices, this ends up being answer choice b. Alright guys. That's it for this one. Let me know if you have any questions.

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1. Intro to Physics Units

Unit Conversions

Physics

1. Intro to Physics Units

Unit Conversions

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Multiple Choice

The speed of light is approximately 3.00×10⁸ m/s. Convert this speed to yards/week (yd/wk).

1.84×10¹³ yd/wk

1.98×10¹⁴ yd/wk

1.78×10¹⁵ yd/wk

1.8×10⁷ yd/wk

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Verified step by step guidance

Start by identifying the conversion factors needed: 1 meter = 1.09361 yards and 1 week = 604800 seconds.

Convert the speed of light from meters per second to yards per second using the conversion factor: \( \text{Speed in yards/second} = 3.00 \times 10^8 \text{ m/s} \times 1.09361 \text{ yd/m} \).

Calculate the speed in yards per second using the conversion factor.

Convert the speed from yards per second to yards per week using the conversion factor: \( \text{Speed in yards/week} = \text{Speed in yards/second} \times 604800 \text{ s/week} \).

Calculate the final speed in yards per week using the conversion factor.