For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a c...

Question

For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics.David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?

Accepted Answer

Hello, everyone. Let's go through this practice problem. Two friends, Ricky and Jessie decided to go cycling. Jessie starts cycling from her house at a constant speed of 10 m per second and she passes Ricky's house at the instant, Ricky begins cycling. Ricky starts from rest and increases his speed at a constant acceleration of 0.5 m per second squared. Draw a pictorial representation along with a motion diagram of this event from Ricky's house to the point he crosses Jesse. OK. So there are no multiple choice options in this problem, but we're asked to draw a couple diagrams of the situation. But the first thing we're asked to draw being a pictorial representation of what's happening. So for the pictorial representation, I'm going to draw a side representation of the, of the road basically. So first off for Jesse, here is the stretch of road and then on the left side is where I will put the starting point, there's like a little uh my crude representation of the bike and we're specifically told by the problem that Jesse is cycling at a constant speed. So for Jesse, there is no acceleration. So a sub J the acceleration of Jesse is zero. And then on the right hand side of the pictograph of the pictorial representation is just where the bike ultimately ends up. Now, let's do the same thing for Ricky. So once again, here is our little road. Here's where the bike starts off from Ricky's perspective. But this time, there is an acceleration, we're told that Ricky starts from rest and increases his speed at a constant acceleration. So there is an acceleration, I'll call it a sub R. And since Ricky is speeding up, that means that the acceleration, the vector is pointed in the direction towards where he's going. So in the context of this diagram, the vector is pointing to the right pointing toward where the bike ends up. And as a pictorial representation of the problem, that's really all we have to do, but we're not done yet because the problem also asks us to draw a motion diagram of the event, which means we'll have to bring the dots in. Remember the motion diagram is what we have when we're representing two vectors with snapshots of where the velo where the positions are after each amount of time based on some time interval. So in the context of this problem, I'm gonna represent that as two different vectors and they can be thought of as snapshots of where the two people are at each point in time. So for Jesse, for example, let's say that the starting point is this point right here. And let's pick a number of points to go with. I'll say there are going to be four more points that Jesse is going to be traveling through. So that's five snapshots in all. And since Jesse is not accelerating is traveling at a constant velocity, then each of these points will be spaced out from one another roughly equally. That is because assuming we choose a constant time interval, there is no reason at all for Jesse to be further at one point from the previous point than they were at an earlier point. So a good motion diagram representing Jesse would look something like this where each of the arrows are roughly equal length. Now we'll do the same thing for Ricky. Now, Ricky as the problem mentions, starts out at rest. So what that means is that Ricky's arrows at the beginning are gonna be kind of short because he's starting from rest and is and is speeding up because of his acceleration. And it is only later that the arrows will start getting longer because he'll be able to cover more ground in the same time interval as before, of course, in, in order to keep things consistent, Ricky's motion diagram should have the same number of points, the same number of snapshots as in Jesse's diagram. But by the end of the diagram, they should be matched up with each other as if they've both hit the finish line since that's how the problem asks us to represent it. So the first point will go some smaller distance for the next snapshot because Ricky is going slower here. But for the next point, he'll be able to go a little bit farther because of the acceleration. And this is a pattern that should continue as Ricky continues to speed up all the way until he reaches the final point. And it should be noted that it doesn't actually matter how many points you choose to use for both Jesse and Ricky. As long as it's the same for both of them. The reason why it doesn't matter how many points you go with is because it depends on what time interval you choose. No matter how long it takes for. We, we could have done the math to determine the exact number of seconds required for Jesse and Ricky to cross paths once again. But no matter how long that takes, we could still divide that number into however many intervals. We want to make this graph really detailed if we really wanted to with a million points, but we don't really have to do that. And since the problem is phrased pretty open endedly, this is a nice simple way to get the point across that still works perfectly fine. So really that is it for this problem? So I hope this video helped you out and I recommend checking out more of our videos which will give you more experience with these types of problems, but that's all for now and I hope you all have a lovely day. Bye bye.

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