1D Kinematics Legacy Problem #22 Guided Solution

On most of these audio-guided solution pages, you're going to see a listing of the habits of an effective problem solver. And each file is going to take you right through those habits and try to train you to practice them yourselves. And here, we're going to begin by just reading the problem, making an effort to visualize what's going on. We're on a miniature golf course, and the ball's rolling up a long, straight incline. It goes into the incline with a given speed of 2.95 meters per second, accelerates at this negative 8.76, the negative meaning it's going to slow down as it's rolling up the hill. And this lasts for 1.54 seconds, and when it gets to the top, it's going to continue rolling along a level, an elevated section. What we're interested in is finding the length of that long, straight upward incline. So I got a picture of this whole thing happening, and I notice it goes in at a given velocity and leaves at some velocity, which I don't know, and I don't know how long it's along the incline. But I know that I can figure it out, because I'm going to use my effective problem-solving habits. I've read it, I've visualized it, and now I'm going to try to write down what I know and express it in terms of variables that I generally find in my equations. I'm going to write down V0 equal 2.95, and I would write it down, don't tell yourself you can just put it on your calculator, write it down. A equal negative 0.876, that's the acceleration, write it down as A equal, t equal, 1.54 seconds. I know three things, I know a V0, I know an A, and I know a t. And I want to know how long that incline is, in other words, what's the distance that the ball rolled along the incline during the 1.54 seconds of travel? Find the d. So I'm going to look for an equation that has within it a d of the original, an A, and a t. And when I find that equation, there's going to be one unknown in it, and I'm going to solve for that unknown. Now if you look carefully at your set of the so-called big four kinematic equations, what you're going to find is there's one equation that goes something like this. t equal, V0, which you know, times t, which you know, plus 1 half A, which you know, times t squared, which you know. And so I know in that equation everything except for the d, and now it just simply involves being careful, substituting it and solving for the d. Now as you do that substitution in algebra, make sure you put a negative acceleration in there. Make sure you put a t in there, and then you square it. And if you do all that, and you're all careful with your order of operation, you're going to get it right.