Final answer:
The area under a velocity vs. time graph represents displacement, slope represents acceleration. To find the area, break the graph into shapes. Total distance traveled is the sum of positive and negative areas. In a position vs. time graph, the slope represents velocity.
Step-by-step explanation:
The area under a velocity vs. time graph represents the displacement of an object. To find the area, you can break the graph into different shapes (triangles, rectangles, etc.) and calculate the area of each shape separately. Add up the areas of all the shapes to find the total area, which represents the displacement.
The slope of a velocity vs. time graph, on the other hand, represents the acceleration of an object. It tells us how the velocity of the object is changing over time. You can find the slope by selecting two points on the graph and calculating the change in velocity divided by the change in time between those points.
To find the total distance traveled, you need to consider both positive and negative areas under the graph. The positive area represents the forward distance traveled, while the negative area represents the backward distance traveled. Add up the absolute values of the positive and negative areas to find the total distance traveled.
In a position vs. time graph, the slope represents the velocity of an object. You can find the slope by selecting two points on the graph and calculating the change in position divided by the change in time between those points.