1D Kinematics Legacy Problem #2 Guided Solution

An effective problem solver, by nature, has a collection of habits which they tend to perform. They may appear to be quick at solving their problems, but for certain, what they are doing is not simply picking up their calculator and plugging numbers into it. The ongoing frustration that is often associated with failing to solve a physics problem can usually be traced back to the habit of simply quickly picking up your calculator, plugging in numbers, and expecting to get a good result. Effective problem solvers tend to do preliminary work before actually picking up their calculator. This preliminary work usually involves reading the problem carefully in an effort to identify what is known and what is unknown. During the process of identifying the known and unknown information, they typically write information down. The most effective problem solvers are so effective at solving their problems, sometimes they even skip this step, but no doubt they at least have the information in their brain. If you are having difficulty solving problems, I would recommend that you use a piece of paper and write some information down. Here in this problem, what we are told is that we have two quantities, we have a quarter mile and we have a time of 4.437 seconds. The quarter mile is a distance and we can express it as .25 miles. What we are being asked to solve for is we are being asked to solve for the average speed, which at first glance you might think is a simple distance over time ratio, and indeed it is. However, there is some preliminary work that we need to do that is associated with the units. The problem asks us to find the average speed in miles per hour and the average speed in meters per second, and what we have is miles in seconds. So the preliminary work involves getting our numerical quantities in the proper unit. We have a d of .25 miles, but we also need to have a d in units of meters. So now you need to think, if 1609 meters is equal to one mile, and we have a quarter of a mile, then what we have is a quarter of 1609 meters. We need to take the 1609 meters and multiply it by .25. That will give us a distance in meters. The next thing we need to do is we need to think about getting a time in units of hours. We currently have it in units of seconds. So now again, you need to think. There are 60 seconds in a minute and 60 minutes in an hour. Plus there are 3600 seconds in an hour. We have 4.437 seconds, far short of an hour. So we need to take this 4.437 seconds and divide it by the 3600 seconds. Now with all this preliminary work finally done, we are able to calculate our answer. The average speed is the distance divided by the time. We can take our miles, which was given, and divide it by the time, which we calculated from the seconds. We divide it by the time in hours and that gives us our average speed in miles per hour. Then what we can do is take our meters, which we calculated from the quarter mile, and divide that by the seconds, which was given, and we get our speed in meters per second.