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Examples of Graph Interp.
Ch 2B Notes
(All velocities in m/s, all time in s)
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1. When is the greatest instantaneous velocity?
• From t = 3 to t = 5
• Furthest from x axis
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2. When is the individual moving in the backwards direction?
• From t = 8 to t = 10 because v vs. t graph is below x-axis
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3. When is acceleration constant?
• t = 0 to t = 3 • t = 3 to t = 5• t = 8 to t = 10• linear
intervals have constant slope
• Constant slope = constant acceleration
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4. When is the instantaneous acceleration = 0?
• From t = 3 to t = 5 because m = 0
• At around 6.2 s because slope of tangent line = 0
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5. Find Ave Accel. from t = 5 to t = 8 s
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5. Find Ave Accel. from t = 5 to t = 8 s
• Find starting point and end point of interval on curve
• Find slope between these points
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Point 1 (5,6)
Point 2 (8,0)
m = Δy / Δx = (y2 – y1) /
(x2 – x1)= (0 - 6) / (8 - 5)= -6 / 3 = -2.0aave = -2.0 m/s2
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6. Find Average Acceleration from t = 0 to t = 4
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6. Find Average Acceleration from t = 0 to t = 4
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m = Δy / Δx
= (y2 – y1) /
(x2 – x1)
= (6-0) / (4-0)
= 6/4 = 1.5
aave = 1.5 m/s2
Point 2 (4,6)
Point 1 (0,0)
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7. Find Instantaneous Accel. at t = 7 s
• Sketch tangent line at point
• Find two points on tangent line
• Find slope
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Point 1 (4,6)8
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Point 2 (9.6,0)
m = Δy / Δx = (y2 – y1) /
(x2 – x1)= (0 - 6) / (9.6 - 4)= -6 / 5.6 = -1.07 m/s2
a7 = -1.07 m/s2
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8. Find Displacement from t = 0 to t = 5 s
• Chop time increments into chunks
• Find area of each chunk
• Sum areas together
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AΔ = 1/2bh = ½ (3)(6) = 9 m
A□ = lw = (2)(6) = 12 m
Atotal = 9 m + 12 m = 21 m
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9. Find Displacement from t = 6 to t = 10 s
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•Create best-estimate shapes of each chunk of area under curve
•Find area of each chunk (below x-axis is negative)
•Sum areas together
A□ = AΔ1 + AΔ2
= ½(2)(4.4) + ½(2)(-8)
= 4.4 m – 8.0 m =
- 4.6 m
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10. Find Average Velocity from t = 3 to t = 6
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1.Find point on curve at beginning and end of interval
2.Find slope between these pointsm = Δy/Δx
= (y2-y1) / (x2-x1)
m = (8-15) / (6-3)
m = -7/3 = -2.33 m/s
Point 1
(3s, 15m) Point 2
(6s, 8m)
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11. Find velocity at t = 6 s• Sketch
tangent line to curve at time desired
• Find two points along tangent line
• Find slope of tangent line using these new points
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Point #1
(3s,19m)
Point #2
(8s,0m)
m = Δy / Δx = (y2 – y1) / (x2 – x1)= (0-19) / (8-3) = -19/5= -3.8 m/s = v6
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12. Find change in velocity from t = 5 to t = 10 s
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•Create geometric shapes that are estimates of the actual area beneath curve•Find area of each chunk•Sum areas together, watching signs
AΔ1 = 1/2bh = ½ (3)(5) = 7.5 m/sAΔ2 = 1/2bh = 1/2(2)(-8) = -8 m/sAtotal = 7.5 m + (-8 m) = -0.5 m/s