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How to Calculate Acceleration Curve on a Graph Tangent

The velocity of an object is how fast the object transitions from one position to another over a specified time interval. The acceleration of an object is the measure of how much the velocity of the object changes over that same time interval. Mathematically speaking, the graph of the acceleration curve describes the slope of the velocity graph from which it is derived. This means that the value of acceleration at a point on its graph is the value of the slope of the tangent line at the same point on the velocity graph. As such, the acceleration graph can be found directly from tangent point values of the velocity graph.

Instructions

- 1
  Find the slope "m" of a given point on the graph of the velocity function using the expression (rise / run) = (Y - y / X - x), Where (x, y) is an initial point, (X, Y) is a second point on the graph and "m" is the slope. For example, solving for the slope between the points (0, 0) and (2, 9) finds: m = (9 - 0) / (2 - 0) = (9 / 2) = 4.5.
- 2
  Convert the slope to a coordinate point by using the value of X as the x-coordinate and the value of m as the y-coordinate. For example, if the slope between the points (0, 0) and (2, 9) equals 4.5 then the new coordinate point becomes (2, 4.5).
- 3
  Find the slope values for several points along the graph of the velocity function.
- 4
  Plot these points on a separate coordinate plane. The more points you have, the more accurately your graph will reflect the behavior of the new graph.
- 5
  Draw a smooth curve connecting all of the points just plotted. The resulting curve is the graph of acceleration from the tangents (slopes) of the velocity function.

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