How to integrate acceleration to get velocity in excel?
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Today's lab will introduce the concepts of numerical integration (area under a curve) via the trapazoid method of approximation and numerical differentiation (slope of a curve) via the finite difference method.Problem
Generate position, veclocity, and acceleration graphs based upon given velocity data.
Initial position: 4 ft.
Time (sec)Velocity (ft/s)02142834405-2Velocity Graph (Video: 5:54 minutes, 10.4 MB)Put Time/Velocity data into Excel (Paste Special)Velocity vs time graph (Select data, Insert, Chart, XY Scatter)Remove background (Format Plot Area)Remove title and legend (Select, Delete)Add labels, grid lines (Chart Options)Move x axis labels to bottom (set Tick Mark Labels to Low), make x axis heavier, make y axis heaver (Right click on axis or tick mark labels, Format Axis)Make curve thicker, remove data markers (Right click on curve, Format Data Series)Position Graph (Video: 8:38 minutes, 14.1 MB)Change in position is the area under the velocity-time curve - approximate area with a trapezoidMove velocity values to column C (Cut/Paste)Use column B for positionInitial position of 4 ft in B2Create formula for position at t=1 in B3 (=B2+0.5*(C2+C3)*(A3-A2))Copy formula down for all time values. (drag/fill)Copy velocity plot (Select border, copy, paste OR ctrl-drag)Change source data and axis labelsAcceleration Graph (Video: 9:10 minutes, 20.3 MB)Acceleration is the slope of the velocity curve - approximate with slope between two pointsGenerate a list of midpoint times in column D - there will be one less row.
[ D2: =(A2+A3)/2 ]Calculate slope of velocity curve in column E
[ E2: =(C3-C2)/(A3-A2) ]Copy velocity plotChange source data and axis labelsChange x axis max to 6 so it will line up with other plots
[right click on axis, Format Axis
Today's lab will introduce the concepts of numerical integration (area under a curve) via the trapazoid method of approximation and numerical differentiation (slope of a curve) via the finite difference method.Problem
Generate position, veclocity, and acceleration graphs based upon given velocity data.
Initial position: 4 ft.
Time (sec)Velocity (ft/s)02142834405-2Velocity Graph (Video: 5:54 minutes, 10.4 MB)Put Time/Velocity data into Excel (Paste Special)Velocity vs time graph (Select data, Insert, Chart, XY Scatter)Remove background (Format Plot Area)Remove title and legend (Select, Delete)Add labels, grid lines (Chart Options)Move x axis labels to bottom (set Tick Mark Labels to Low), make x axis heavier, make y axis heaver (Right click on axis or tick mark labels, Format Axis)Make curve thicker, remove data markers (Right click on curve, Format Data Series)Position Graph (Video: 8:38 minutes, 14.1 MB)Change in position is the area under the velocity-time curve - approximate area with a trapezoidMove velocity values to column C (Cut/Paste)Use column B for positionInitial position of 4 ft in B2Create formula for position at t=1 in B3 (=B2+0.5*(C2+C3)*(A3-A2))Copy formula down for all time values. (drag/fill)Copy velocity plot (Select border, copy, paste OR ctrl-drag)Change source data and axis labelsAcceleration Graph (Video: 9:10 minutes, 20.3 MB)Acceleration is the slope of the velocity curve - approximate with slope between two pointsGenerate a list of midpoint times in column D - there will be one less row.
[ D2: =(A2+A3)/2 ]Calculate slope of velocity curve in column E
[ E2: =(C3-C2)/(A3-A2) ]Copy velocity plotChange source data and axis labelsChange x axis max to 6 so it will line up with other plots
[right click on axis, Format Axis
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