1D Kinematics Legacy Problem #9 Guided Solution

There's a couple of ways to solve this problem. One of them is quite easy and the other one is significantly harder. Now, given the placement of the problem, where it is in the problem set, I'm going to presume that most people have not yet heard of the kinematic equations, or the so-called big four. If you have, that's the easy way to solve this problem, because what you have is an original velocity, a final velocity, and a distance, and you're asked to calculate an acceleration. So you're given three of the four variables within a kinematic equation. But presuming that you've not yet learned of the kinematic equations, I'm going to approach this problem the hard way. And in the hard way to solve this problem, what you're going to do is calculate the acceleration by determining a velocity change in a time. Now, the velocity change is quite simple, because what we have is a race car that decelerates from an original velocity of 27.8 meters per second to a final velocity of zero. But what we don't have is we don't have the time. So what we're going to try to do is calculate the time using a second equation. That second equation is the average speed equation. I can find my average speed by taking the two extremities, the 27.8 and the zero, the two extremities of speed, and averaging them. That would give me an average speed of about 14.9 meters per second. I'm going to correct that, 13.9 meters per second. And I can use my average speed equation that 13.9 meters per second is equal to the distance of 17 over time. And I can solve for the time that it takes this car to decelerate to a stop. Now, once I get my time, I can then use my acceleration equation, delta v over t, and solve for the acceleration. That method makes this a significantly more difficult problem, because first of all, you have to think of the strategy, and second of all, you have to operate and execute the mathematics.