(a) Complete the motion diagram by adding acceleration vectors.

Video transcript

Hey, everyone in this problem, we have a motion diagram that represents the velocity and acceleration of an object at several different times. And we're asked to add the acceleration vectors to the motion diagram we were given in order to complete it. So we have this U shaped motion diagram and the arrows are pointing to the right throughout this entire diagram. Starting on the left hand side, we have these arrows that are close together and getting further apart. OK. Our points are getting further apart. What that means is that in the same amount of time this object is traveling further. OK. That means the velocity is getting bigger if the velocity is getting bigger, that means we must have a positive acceleration or acceleration that's acting in the same direction as the motion. OK. So in this portion of our diagram, we're gonna have the acceleration acting along that motion. Hm Now we get to a point in our diagram where those points start to get closer together again, still moving to the right but getting closer together, they're getting closer together. That means that it's slowing down. And that means that the acceleration must be opposing the motion. OK. So when we have acceleration, opposing the motion, the arrows are gonna point in the opposite direction. So for this portion of our diagram, we have the arrows pointing in the opposite direction, they're gonna be pointing up to the left instead of down to the right. And this is gonna continue until we get to the bottom of that. E Now once we get to the bottom of that U yeah, these arrows are, or these points are about the same distance apart, they're not spreading apart anymore. So when we're talking about the acceleration to the right or to the left, we really don't have an acceleration in that direction and acceleration is gonna be zero. However, our object is gonna start moving upwards immediately after this. So we must have some sort of upward acceleration. And so through this portion of our motion diagram, we're gonna have this acceleration that's pointing upwards a little bit. Now moving to the next part of our diagram, we're going upwards in this U on the right side, our points are starting to get further apart. Again, that means acceleration is acting with the motion. And so it's gonna follow the same arrows as our velocity all the way up. And again, we get to a point where those points start to get closer together. Remember closer points means less distance traveled in the same amount of time. That means a smaller velocity. And that means that the acceleration must be opposing the motion if the velocity is slowing down. And so for the final part of our diagram, we have the acceleration pointing down to the left opposing that motion and that's it. So for that diagram, we've added the acceleration vector throughout the entire part and that's the answer to the question. I hope this video helped. Thanks everyone for watching. See you in the next one.