1. The problem statement, all variables and given/known data The diagram shows different phenomena when velocity vector and acceleration vector are on the same graph. The first graph which is pretty simple is when acceleration and velocity are pointing in the same direction. This means that the object's speed is increasing. The second graph shows acceleration pointing up in the y axis and velocity vector pointing to the right on the x axis. This represents constant speed for the object. I can visually understand the above two demonstrations; however, the next two diagrams really confuses me. The acceleration vector is now in between 0 degrees and 90 degrees pointing diagonally having a x and y coordinate, while the velocity vector is pointing to the right on the x-axis. The last diagram is similar in that the velocity vector is pointing to the right on the x axis while the acceleration vector is pointing diagonally in between 90 degrees and 180 degrees. In what situation does this actually occur in real life. I can't seem to visualize this phenomena. 2. Relevant equations In the book they give an example in which the acceleration is pointing diagonally in between 270 degrees and 360 degrees and the velocity vector in the direction pointing right on the x-axis. This is their explanation. The component of acceleration parallel points along the line of the objects motion, so the speed of the object will change; in particular, the speed will increase, since a parallel points in the same direction as v. The component of a that's perpendicular to v, will make the direction of v change; in particular, it will turn downward(since a perpendicular points downward). Therefore, we'd expect the object to increase in speed as it turns downward. I don't understand the last part, as i cannot see its relative starting point and as i cannot visualize this process. 3. The attempt at a solution I think it might have something to do with centripetal acceleration, or when an object is curving. I am not really sure.