1D Kinematics Legacy Problem #3 Guided Solution

Physics problems typically begin as word problems and the end as mathematical exercises. And most often, student difficulty occurs way before the actual mathematical operations take place. The problem isn't actually in the act of using your calculator and calculating the answer, but it's in the transforming of the word problem into a mathematical exercise. The task of successfully transforming a word problem into a mathematical exercise involves carefully reading the problem, trying to figure out what's being asked, what's being given, and then doing some good conceptual thinking in order to change this problem into a math problem. In this problem, we read about a swimmer who is swimming a 50-yard freestyle. It's done in a 25-yard pool, evidently, which is very common for high school swimming pools. So the swimmer is swimming 25 yards down, does it in 10.01 seconds, then comes back 25 yards, finishing where the swimmer started. The time for the second leg of the trip is also given. So the picture in my mind here is of a down-and-back motion, and I'm asked three questions about this motion. The first question has to do with average speed. What I need to know is the distance-time ratio for the entire race. The entire race being characterized by a 50-yard distance of travel and a time that can be found by adding the time for the two legs, the 10.01 seconds plus the 10.22 seconds. This gives me an average speed calculation as a 50 yards divided by this 20.23 seconds. The second part of the problem involves focusing on the first 25-yard leg of the trip. So it's 25 yards down in 2.01 seconds, and that's a straightforward calculation. With both the numerical quantities given, take the 25.00 yards divided by the 10.01 seconds, and you'll get an answer for the average speed. It would be in units of yards per second. That's fine. Now the third part of the problem is a part that's a real twist. In getting this part C correct, what you need to do is you need to understand the distinction between average velocity and average speed. The average velocity is a ratio of a displacement over time. For a down-and-back trip, the displacement would be 0 yards. If they were asked what's the average speed for the entire race, it would be the same question as A, where average speed is a distance, total distance traveled, divided by time. So getting the answer C involves very little in the way of calculation, and a great deal in terms of understanding the concept of average velocity and its distinction between average speed.