1D Kinematics Legacy Problem #5 Guided Solution

Effective problem solvers typically have a collection of habits that they practice by nature. Those habits involve reading the problem carefully and visualizing what's going on with the physical situation. Then identifying the known and unknown information, expressed usually in terms of variables that we find in our physics equation. Finally, they tend to plot a strategy for getting from the known information to the unknown information. Finally, they begin to use a calculator. So here, as I read this problem, what I recognize is that we have an object that is given an initial speed and is going to slow down to a stop. I've been given the V original and the V final, which is zero because it's slowing down to a stop. And I've been given the acceleration rate. It's negative, consistent with the idea of slowing down. I'm asked to find two things. The time it takes to slow to a stop. And then finally, the distance that it travels before stopping. And I'm given some clues there that I should use my initial speed, my final speed, and my calculated time to get an average speed. And use the average speed equation. We'll talk about step A first. So, what I'm going to do is I'm going to equate the numerical information. There's three pieces of information here. The 9.32 meters per second, the negative 4.06 meters per second per second, and then the stop. I'm going to connect those three pieces of information with some variables. I'll say that V initial, or V0, is equal to 9.32. I'll say that V final, Vf, is equal to zero. Thus, the delta V is going to be the final minus the initial. It's going to be a negative 9.32 meters per second. And I'm going to equate the negative 4.06 with the A. A equals negative 4.06. Now, in the strategy plotting phase, I'm going to look for an equation that has the three things I'm looking for. Or at least the one thing I'm looking for, the two things I know. I'm looking to have the time. And I know the delta V and the A. The relevant equation is A equals delta V over the T. I need to stick my given A on the left side of that equation. And I need to stick my delta V in the numerator on the right side. I'm solving for a quantity in the denominator, which means I'll have to be careful with my algebra. Typical algebra involves multiplying both sides of the equation by the T, such that the equation becomes 4.06T is equal to 9.32, and then dividing each side of the equation by the negative 4.06. I end up getting a time out of that. That's how you do step A. Step B is a little bit more complicated. You have to kind of read it again carefully. Look what they're asking you to do. Determine the average speed, and then use that to calculate the distance. Well, the average speed for a constant acceleration motion is just going to be the final plus the initial divided by 2. Take the two extremes and average them. So that ends up being 9.32 divided by the 2. When I do that, I get my average speed. And then I'm going to say average speed is distance over time. And I've just found the time from part A. I will rearrange that equation to D equal the average speed multiplied by the time. And I got my answer.