Calculating Displacement from Velocity vs. Time Graph
Learn how to determine displacement from a velocity vs. time graph by calculating the area under the graph for specific time intervals. Explore examples and understand how to calculate total displacement over different time periods.
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Velocity vs time graph Calculating the area under the graph Displacement
Calculate the displacement for a specific time interval on a velocity vs time graph The area under the graph is the displacement Area = (base)(height) Area = (lenght)(width)
Graph 1Determine the area under the graph for each segment +15 m/s +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 1Determine the area under the graph for each segment +15 m/s +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 1What is the total displacement from 0 to 6 s? Imagine the shapes from the curve to the 0m/s line +15 m/s +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 1 From 0 to 2 s Displacement=Area = (base)(height) displacement= ( 2s)(+10m/s) +15 m/s Displacement = (+20m ) Displacement= +10m +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
From 2 to 5 s Graph 1 Displacement=Area = (length)( width) displacement= ( 3s)(+10m/s) Displacement = (+30m ) +15 m/s Displacement= +30m +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 1 From 5 to 6s Displacement=Area = (base)(height) displacement= ( 1s)(+10m/s) +15 m/s Displacement = (+10m ) Displacement= + 5m +10 m/s velocity +5m/s 0 m/s -5 m/s -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 1What is the total displacment from 0 to 6 s? +30m + 5m +15 m/s +10m +10 m/s velocity +5m/s 0 m/s Total displacement= +10m + +30m+ +5m= -5 m/s 45 m -10 m/s 2 s 3 s 0 s 1 s 4 s 5 s 6 s time
Graph 2 Find the displacement from to 0 to 10 s, 10 to 20 s, 20s to 30 s +6 m/s +4 m/s velocity +2m/s 0 m/s -2 m/s -4 m/s 10 s 15 s 0 s 5 s 20s 25 s 30 s time
Graph 2 Find the displacement from to 0 to 10 s, 10 to 20 s, 20s to 30 s Imagine the shapes from the curve to the 0m/s line +6 m/s +4 m/s velocity +2m/s 0 m/s -2 m/s -4 m/s 10 s 15 s 0 s 5 s 20 s 25 s 30 s time
Graph 2 From 0 to 10 s Displacement=Area = (length)( width) displacement= ( 10s)(+4m/s) +6 m/s Displacement = (+40m ) Displacement= +40m +4 m/s velocity +2m/s 0 m/s -2 m/s -4 m/s 10 s 15 s 0 s 5 s 20 s 25s 30 s time
Graph 2 From 10 to 20 s Displacement=Area = (base)(height) displacement= ( 10s)(+4m/s) +6 m/s Displacement = (+40m ) Displacement= +20m +4 m/s velocity +2m/s 0 m/s -2 m/s -4 m/s 10 s 25 s 0 s 5 s 20 s 25s 30 s time
Graph 2 From 20 to 30 s Displacement=Area = (base)(height) displacement= ( 10s)(-4m/s) +6 m/s Displacement = (-40m ) Displacement= -20m +4 m/s velocity +2m/s 0 m/s -2 m/s -4 m/s 10 s 15 s 0 s 5 s 20 s 25 s 30 s time
Graph 2 +6 m/s +40m +20m -20m +4 m/s velocity +2m/s 0 m/s -2 m/s Total displacement= (+40m) + (+20m) + (-20m) +40 m -4 m/s 10 s 15 s 0 s 5 s 20 s 25 s 30 s time
Graph 3 Find the displacement from0 to 30s, 30 to 50s, 50 to60 s Find the displacement for the entire graph +30m/s +20 m/s velocity +10m/s 0 m/s -10 m/s -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
Graph 3 Find the displacement from 0 to 30s, 30 to 50s, 50 to60 s Imagine the shapes from the curve to the 0m/s line Find the displacement for the entire graph +30m/s +20 m/s velocity +10m/s 0 m/s -10 m/s -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
From 0 to 30 s Displacement=Area = (base)(height) displacement= ( 30s)(+10m/s) Displacement = (+300m ) Displacement= +150m Graph 3 +30m/s +20 m/s From 0 to 30 s Displacement=Area = (length)( width) displacement= ( 30s)(+10m/s) Displacement = (+300m ) Displacement= +300m velocity +10m/s 0 m/s -10 m/s Total displacement from 0 to 30 s = (+150 m) + (+300m) = 450m -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
Graph 3 From 30 to 50 s Displacement=Area = (length)( width) displacement= ( 20s)(+10m/s) Displacement = (+200m ) Displacement= +200m +30m/s +20 m/s velocity +10m/s 0 m/s -10 m/s -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
From 50 to 60 s Displacement=Area = (base)(height) displacement= ( 10s)(+20m/s) Displacement = (+200m ) Displacement= +100m Graph 3 +30m/s +20 m/s From 50 to 60 s Displacement=Area = (length)( width) displacement= ( 10s)(+10m/s) Displacement = (+100m ) Displacement= +100m velocity +10m/s 0 m/s Total displacement= (+100 m) + (+100m) -10 m/s = +200 m -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
Graph 3 Find the displacement from 0 to 30s, 30 to 50s, 50 to60 s Find the displacement for the entire graph +30m/s +450 m +200m +20 m/s +200m velocity +10m/s 0 m/s Total displacement = (+450m) + (+200m) + (+200m)= -10 m/s 850m -20 m/s 20 s 30 s 0 s 10 s 40 s 50 s 60 s time
Graph 4 Calculate the total displacement for the graph below +300m/s +200 m/s velocity +100m/s 0 m/s -100 m/s -200 m/s 4 s 6 s 0 s 2 s 8 s 10 s 12 s time
Graph 4 Calculate the total displacement for the graph below Imagine the shapes from the curve to the 0m/s line +300m/s +200 m/s velocity +100m/s 0 m/s -100 m/s -200 m/s 4 s 6 s 0 s 2 s 8 s 10 s 12 s time
Graph 4 Calculate the total displacement for the graph below +300m/s +200 m/s From 0 to 5s Displacement=Area = (base) (height) displacement= ( 5s)(-200m/s) Displacement = (-1000m ) Displacement= -500m velocity +100m/s 0 m/s -100 m/s -200 m/s 4 s 6 s 0 s 2 s 8 s 10 s 12 s time
Graph 4 +300m/s From 5 to 12 s Displacement=Area = (base)(height) displacement= ( 7s)(+300m/s) Displacement = (+2100m ) +200 m/s velocity +100m/s Displacement= +1050 m 0 m/s -100 m/s -200 m/s 4 s 6 s 0 s 2 s 8 s 10 s 12 s time
Graph 4 Calculate the total displacement for the graph below +300m/s +1050 m +200 m/s velocity -500m +100m/s 0 m/s Total displacement = (-500m) + (+1050m) = +550m -100 m/s -200 m/s 4 s 6 s 0 s 2 s 8 s 10 s 12 s time
But what if the curve on a graph is actually a curve?
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