# Based on this graph estimate the total distance traveled during the flight from the take off to the landing on the beach. A GPS recorded the following graph of the velocity function v(t). Based on...

• Based on this graph estimate the total distance traveled during the flight from the take off to the landing on the beach.
• A GPS recorded the following graph of the velocity function v(t). Based on this graph estimate the total distance traveled during the glider flight from the take off to the landing on the beach. Explain in words how you do this estimate.

lfryerda | High School Teacher | (Level 2) Educator

Posted on

Since your graph is a velocity vs time graph `v(t)` and distance is the integral of velocity, that is since `int v(t)dt`, then you need to estimate the integral of the graph.  We can do this with approximating the graph using rectangles, then adding up the areas of each rectangle.

From the grid, you see that there are some natural rectangles we can use.

The first rectangle goes from (0,0) to (1,0) to (1,2) to (0,2) with an area of 2.

The second rectangle goes from (1,0) to (2,0) to (2,1.5) to (1,1.5) with an area of 1.5.

The third rectangle is from (2,0) to (3,0) to (3,1) to (2,1) with an area of 1.

And the fourth rectangle is from (3,0) to (4,0) to (4,3.5) to (3,3.5) with an area of 3.5.

This means the area under the curve (which is the distance for your question) is 2+1.5+1+3.5=8.

The total distance is the sum of all the rectangles from the graph which is 8 units.

cspanutius | Student, Undergraduate | (Level 1) Salutatorian

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[url=http://postimage.org/image/vs7g1d2cv/][img]http://s19.postimage.org/vs7g1d2cv/calc_hw_21_graph_for_6.png[/img][/url]

[url=http://postimage.org/image/bm3y2h6pb/][img]http://s19.postimage.org/bm3y2h6pb/calc_hw_21_graph_for_7.gif[/img][/url]

cspanutius | Student, Undergraduate | (Level 1) Salutatorian

Posted on

I am trying to insert a graph for the question above... can anyone tell me how to do it