How do I find the displacement of an object using a velocity vs. time graph?
I also need to draw position and acceleration graphs. How do I ensure they look accurate based on the velocity graph?
Answer (4)
So you HAVE a velocity/time graph, and you want to use it to construct other graphs.
-- Displacement. On the velocity/time graph, mark the beginning and end of some period of time. The displacement of the object during that time is the area between those two times, and between the graph and the x- (time-) axis. In places where the graph is above the x-axis, the area adds to the total. If there are any places where the graph is below the x-axis then that much area subtracts from the total (because negative velocity means moving backwards, so naturally the displacement is getting smaller during that part of the time).
-- Position. This is tedious. The position at each point comes from the displacement at each point in time. That means doing the area thing from the beginning of time to each point in time, and then put a point at that time on the position graph. Each time you do the area thing, it gives you one point to put on the position/time graph.
-- Acceleration. The acceleration at any time is the slope of the velocity/time graph at that time. If the velocity/time graph is a straight line, then it has the same slope everywhere on it, the acceleration is constant, and you don't need to draw a new graph of acceleration. If the velocity/time graph has any breaks or curves in it, then the acceleration isn't constant. You have to find the slope at several different points on the velocity/time graph. The slope at each different time gives you one point to put at the same time on the acceleration/time graph.
To find the displacement using a velocity vs. time graph, calculate the area under the curve. The position and acceleration graphs can be obtained by taking the integral and derivative of the velocity graph, respectively. ;
To find the displacement using a velocity vs. time graph, calculate the area under the curve. The position and acceleration graphs can be obtained by taking the integral and derivative of the velocity graph, respectively. ;
To find displacement from a velocity vs. time graph, calculate the area under the graph between the specified time interval, noting positive and negative areas. To create position and acceleration graphs, use the area for position and slopes for acceleration, ensuring these are plotted accurately. These relationships depict how displacement, velocity, and acceleration interrelate in motion analysis.
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