Suppose that an object is attached to a spring and is started in motion so that the speed at time t is given by |5cos(t)| . How far did the object travel from t=0 to t=2蟺? (Use the Fundamental Theorem of Calculus)Suppose that an object is attached to a spring and is started in motion so that the speed at time t is given ?
The above answer is correct, only a mistake occurs in the calculation of the last integral. It should read:
. 2蟺
. .鈭? 5x.dx = 5, (instead of = 10)
3蟺/2
The total distance traveled will be: 5 + 10 + 5 = 20Suppose that an object is attached to a spring and is started in motion so that the speed at time t is given ?
Integral of [|5cos(t)|]dt from 0 to 2蟺 it is equal to
Integral of [5cos(t)]dt from 0 to 蟺/2 + Integral of [-5cos(t)]dt from 蟺/2 to 3蟺/2 + Integral of [5cos(t)]dt from 3蟺/2 to 2蟺
=[5sint](0 to 蟺/2) +[-5sint]( 蟺/2 to 3蟺/2)+ [5sint](3蟺/2to 2蟺)
= 5+10+10 = 25 units
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