A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0?
2 answers:
Answer:
It goes to zero three times
Step-by-step explanation:
s(t) = e^ cos(x)
To find the velocity, we have to take the derivative of the position
ds/dt = -sin x e^ cos x dx/dt
Now we need to find when this is equal to 0
0 = -sin x e^ cos x
Using the zero product property
-sin x=0 e^cos x= 0
sin x = 0
Taking the arcsin of each side
arcsin sinx= arcsin 0
x = 0 ,pi, 2 pi
e^cos x= 0
Never goes to zero
Answer:
The velocity is equal to 0 for 3 times.
Step-by-step explanation:
Given position function s = ecos(x)
Its velocity function, s' = ds/dt = e(-sinx)dx/dt
Between [0,2π], s'=0, -e(sinx)dx/dt=0
sinx=0
x=0, π, 2π
The velocity is equal to 0 for 3 times.
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