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How to Make a Velocity Graph From an Acceleration Graph

Mathematics can be divided into a number of sub-disciplines including calculus, statistics and mechanics. Mechanics is the study of moving bodies and the use of mathematical expressions to predict body trajectories. Three of the most important quantities in mechanics are position, velocity and acceleration. These quantities are often plotted on a graph in order to visualize how a body moves with time. Once you plot the acceleration, you can generate the velocity graph.

Things You'll Need

Graph paper
Ruler

Instructions

- 1
  Draw vertical lines between the x-axis and the curve on the time-acceleration graph, using a ruler. Use a spacing (h) of approximately 2 seconds on the x-axis. Once complete, the area under the graph should be divided into strips.
- 2
  Calculate the area within each strip. The area in each section is equal to the average velocity over that time. In order to find the area for each strip, use the trapezium rule. For each strip, find the y values on the curve at the beginning and end of the strip. For example, at x=0 y may be 4 and at x=2 y may be 6. The formula to find the area given these points is: Area = h/2 (y0 +2y1) where h is the spacing on the x axis (2), y0 is the y0 value at x=0, and y1 is the value at x=2. Following the example, the area of the segment would be:
  
  Area = 2 /2 (4 + (2*6) = 16 meters/second.
  
  Hence the average velocity between x=0 and x=2 equals 16m/s. Repeat this step for each of the segments on the graph.
- 3
  Draw a table to show the values of the area (or velocity) for each segment. In the first column place the average time (i.e., the point on the x-axis where the area was found). In the second column place the area (velocity). For example:
  
  Time (s)=2 Area/Velocity (m/s)=16 Coordinates (2,16)
  
  Time (s)=4 Area/Velocity (m/s)=20 Coordinates (4,20)
  
  Time (s)=6 Area/Velocity (m/s)=20 Coordinates (6,20)
  
  Time (s)=8 Area/Velocity (m/s)=16 Coordinates (8,16)
  
  Draw a graph and label the x-axis "Time (s)" and the y-axis "Velocity (m/s). For the first set of coordinates in the table find where the x and y value intersect, and place a cross at that point. Repeat this for the remaining points. Use a ruler to join adjacent points. The velocity graph has now been generated from the acceleration graph.

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