When you use a graph to solve a problem about how far a car traveled during a specified time during which it

Question

was accelerating how many area calculations do you have to make ?what is/are the shape/shapes you are calculating?

Answer 1

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If the acceleration is constant, and you are concerned ONLY with distance traveled during the acceleration, you can use the equation

s = v0t + (1/2)at^2

which, strictly speaking, requires 5 calculations.  You can do it in 4 calculations if you factor a "t" out and use

s = t(v0 + (1/2)at).

In this example you are calculating the shapes of a rectangle and a triangle if the graph is a graph of velocity.

If the acceleration is not constant, you can still approximate the area under the graph with the area of small trapezoids or rectangles.  Then the number of calculations you need depends on the accuracy you desire.