https://youtu.be/V0PcW6Tk0bE
PHYS 1101: Lecture Five, Part Seven
All right. The next example, I’m actually just going to ask you several quiz questions to see if you understand what going through these steps is, and to do it for a problem on your own.
So here’s a problem where a car starts from rest. It’s heading due east. It first accelerates at 3.0 meters per second squared for 5.0 seconds. Then it continues on without further acceleration for the next 20 seconds. I interpret that to mean that whatever velocity I’ve gotten up to with this initial acceleration, I then hit the cruise control, and I stay at that velocity for the next 20 seconds. I’m going in a straight line at constant speed. After that 20 seconds — so this is 25 seconds after we’ve started — the car then hits the brakes for the next 8.0 seconds, in coming to a rest.
Boy, right away when I read this, I’m picturing a motion diagram. The car’s going fast. It’s coming to a rest. It’s coming to a stop. It’s got to be slowing down. My spots have to now be getting closer together.
This problem would have you solve for the car’s velocity after the first 5.0 seconds. What’s the car’s acceleration during the last 8.0-second time interval? And then a question putting it all together: What’s the total displacement? And remember, the total displacement would be the vector that has to start right at the beginning, where this car started from rest, and go all the way to the very end after coming to a rest in this last 8.0-second interval.
You’d want the total displacement, so let me just sketch on here. This might be where the car was, perhaps, after the first 5 seconds. It cruises along, maybe here. This is 25 seconds later. So on this displacement vector, I’m just kind of doing a quick mental sketch that I want this total length over that whole time interval: the first 5 seconds, the intermediate 20 seconds, and the last 8. That’s what they want for (c).
Okay. So, here’s some quiz questions. I just want you to go through these. Think them through on your own. What object is the focus here?
Next question, 6, is the acceleration constant during the scope of the entire motion described: over the first 5 seconds, the next 20, and the last 8?
Question 7. I have a selection here of motion diagrams for you. Now, because of the time interval difference — for example, this intermediate time, it’s actually 20 seconds long, although you wouldn’t guess that from just the motion diagram. But compare between these three. There’s only one that matches the motion most correctly. Which one is it? What’s the general trend throughout this motion? Do I ever have constant velocity, and it’s speeding up, or slowing down? Which of these is right?
Question 8. You have to work this problem in parts. You must treat each interval with constant acceleration separately, including the interval during which, if there is one, a is 0. So how many parts are there to this problem? That’s Question 8.
Try your hand at working through this problem on your own. I won’t put a quiz question here about any specific numbers or answers. When I go back through this lecture and walk you through the solutions to your quiz questions, I’ll go ahead and work out this problem, and you can then compare my solution to your solution. That would be a good exercise for you.