Question

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?

Answer 1

The velocity is equal to 0 for 3 times.

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.

Answer 2

It goes to zero three times

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