1D Kinematics Legacy Problem #11 Guided Solution

There are many ways to describe the motion of an object, and in this case, we have the motion of a physics teacher being described with a position time graph. And in this position time graph, what we notice is there's a line sloping upwards for the first five seconds, and then sloping downwards for the last three seconds, representing a teacher who walks from the front of the classroom to the back of the lab, and then comes back up to the middle of the classroom. So the upward sloping line is the motion of the teacher from the front of the classroom to the back of the lab, and the downward sloping line is for the return of that teacher in the middle of the room. We're asked five questions about this object's motion. First, we're asked, what's the total distance walked for the entire eight seconds? So we have to conceptualize what's going on in this graph. We have a teacher for five seconds changing his position from a one meter location, one meter from the front of the room, to an eleven meter position, eleven meters from the front of the room. Now that's a position change from one to eleven meters. That's a ten meter position change in five meters, or in five seconds. And then the teacher walks forward, but not all the way forward, but forward to the five meter mark. That's from eleven meters to five meters in the last three seconds. That's six meters in three seconds. Now we have five questions to answer. The first one is, what's the total distance walked by the coach? And that's just simply the ten meters to the back of the room, plus the six meters to the front of the room. That's sixteen meters total. The next question, what's the average speed during these eight seconds? Well, that's just simply the ratio of the distance to the time, the total distance traveled to the total time. And that's just simply sixteen meters over eight seconds, or two meters per second. Now the next question is distinctly different. What's the average velocity for the eight seconds? So what we need to do is calculate an overall displacement of the coach, who started one meter from the front of the room and finished six meters from the front of the room, or five meters from the front of the room. Well, that's an overall displacement from one to five, or a total displacement of four meters. That takes place in eight seconds. So the coach has displaced, or the teacher has displaced himself four meters in eight seconds. That gives you an average velocity of point five meters per second. Finally, I want to know how fast he walked in the first five seconds and then in the last three seconds. Those are distance to time ratios. So he walked ten meters in five seconds. That's two meters per second. And then walked six meters in three seconds. That also is two meters per second.