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V. Finding displacement using V vs t graphs
since V = Δd/t
then Δd = Vt = Area under the plot = displacement (distance)
Ex) What is the displacement this object covered from t = 0 to t = 6 seconds?
d = Area of the triangle:
= 1/2bh
= 1/2(6 sec)(70m/sec)
= 210 m
Ex 1) Object's displacement from
d = Area = base x height
= (2 sec)(10 m/sec) = 20 m
Ex 2) Object's displacement from t = 6 sec to t = 8 sec ? d = area of trapezoid
= 1/2 (h_{1} + h_{2}) x base
= 35 m
AP Question Ex 3) a) Find displacement after 4 seconds b) At what time does the object return to its starting point?
After 4 seconds: 1/2(3 sec)10 m/s + 1/2(1 sec)10 m/s 15 m + 5 m = 10 m
Answer: 5 seconds when d = 0
Ex 4) When did car A catch up to car B?
Car A caught up to car B when their d are equal
At 60 sec: Car B: d= 60 m/s(30 sec) = 180 m Car A: d =1/2(60 m/s)(60 sec) = 180 m
ŠTony Mangiacapre.,
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