How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

Video transcript

Hey, everyone in this problem, a cyclist with constant acceleration speeds up from zero mph to 22 mph. In 42.6 seconds were asked to determine the length covered By the cyclist. The moment they attained 22 mph were told to express our answer in SI units and in feet, The answer traces were given are a 209 m, 687 ft. B 210 m, 64 ft C4.9, 2 m, 16.1 ft ND 4.92 m 1.5 ft. Now, we're told that we have constant acceleration. What that means is that we can use our, you am equations or our Kinnah Matic equations if that's how you're professor likes to call them. So let's write out all of the variables and fill in the information. We know our initial speed. V not, It's gonna be zero mph. Our final speed VF Is equal to 22 mph. We don't know anything about the acceleration. We don't know the distance traveled, but this is what we'd like to find, We're told that the time that this takes is 42.6 seconds. Alright. So we have three known values V not V F and T. One thing we want to find is a distance C or the length covered. Okay. So we can use those equations, we just choose the equation with the variables of interest and substitute in our values. Now, before we do that, let's go ahead and convert into meters per second are standard unit. Since the question is asking us to find both S I units and feet, let's go ahead and convert this into our standard unit first. So zero MPH, that one's easy because it's going to be zero m per second as well. Okay, the speed is zero no matter how you're measuring it. Now, when we go 22 mph, let's write this out as 22 miles divided by our. Now we're going to multiply this. We know that there's one hour in every hour, there is 3600 seconds. We have one hour divided by 3600 seconds. Now, because these two are equivalent, what we're doing is essentially multiplying this by one, which doesn't change the value. Now, the unit of our will divide out and now we're left with miles per second. All right. Now, we want to convert the miles into meters in order to do that, we multiply by 1,609. m per were divided by a mile. The unit of mile will now cancel or divide out and we're left with meters per second. So we have 22 divided by 3600 multiplied by 1609.344. And this gives us a value of 9. 4, 8 m/s. And always check with your professor on the number of significant digits they like for you to carry throughout a problem. Okay. In this case, we've kept quite a few but it, it does depend on the textbook you're using. And the professor that you have how many they like you to carry through in these intermediate steps? Alright, so we have all of our variables there in the units we want, let's choose an equation. We know V not V F and T we're looking for D we're not given any information about the acceleration A and that's not what we're trying to find. So let's choose the equation that doesn't include the acceleration A and that equation is going to be D is equal to one half V, not who wants to be a times the time T This is gonna be equal to 1/2 Times 9.8, 3, 488 meters per second. Okay? Because V not is zero. So we just have VF times of time T 42.6 seconds And this gives us a distance d of 209. m. Alright. So that is our distance in R S I unit. Now we want to go ahead and convert this into feet as well. So in order to convert in defeat And we're gonna take our distance in m and we're gonna multiply it by 3.28 ft okay per one m. So 3.28 ft divided by one m The unit of meter will divide out. We're gonna be left with a value of 687. ft. Okay. And that is the value we were looking for. And no, I want to make one comment here in this problem. We've used the equation that doesn't include the acceleration A and that is the quickest and most efficient way to solve this problem, which is why I showed you like this. There are some cases where your textbook will not include this equation as one of the kid a Matic equations. It's rare but sometimes textbooks or professors don't like to use this equation. If that's the case, you can still solve the problem. What you need to do is use V not V F and T to first find the acceleration A using one of the other equations. And then once you have the acceleration A, you can choose any of the other equations to find the distance D okay. So it's still possible. There's just a little bit, a few more steps to do on the way. Alright, so we found our answer. We compared to the answer choices, we found that the distance or the length covered by the cyclist is about 209 m or 687 ft, which corresponds with answer choice. A that's it for this one. Thanks everyone for watching. See you in the next video.