To obtain acceleration from a velocity vs. displacement graph, you can use the concept of instantaneous acceleration. Instantaneous acceleration represents the rate at which velocity is changing at a specific point in time or position.
Here's a step-by-step process to find acceleration from a velocity vs. displacement graph:
Examine the graph: Look at the shape and characteristics of the velocity vs. displacement graph. The graph should represent the relationship between velocity and displacement over time.
Calculate the slope: Determine the slope of the velocity vs. displacement graph at a specific point. The slope represents the velocity change per unit displacement. You can calculate the slope by selecting two points on the graph that are close together and finding the ratio of the change in velocity to the change in displacement.
Repeat for multiple points: To obtain a more accurate representation of acceleration, calculate the slope at various points along the graph. Select different points that are close together and find the slope for each of them.
Interpret the slope: The slope of the velocity vs. displacement graph represents the instantaneous acceleration at that specific point. If the slope is positive, it indicates positive acceleration (speeding up), while a negative slope represents negative acceleration (slowing down). The magnitude of the slope corresponds to the magnitude of acceleration.
Note that this method assumes a continuous and smooth velocity vs. displacement graph. If the graph has abrupt changes or irregularities, the instantaneous acceleration may not be well-defined at those points.
It's worth mentioning that if you have access to the time data as well, it may be more accurate to calculate acceleration using the change in velocity over time (using the formula a = Δv/Δt). However, if you only have a velocity vs. displacement graph, the method described above can provide an estimation of the instantaneous acceleration at different points along the graph.