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The shadow of a pendulum cast on a flat board moves on a straight line. By placing the x-axis on the straight line with the origin at the middle of the total path, the x-coordinate of the shadow is given by the following function: x(t) = 45cos(πt), where t is in seconds and x is in centimeters.show answer No Attempt 25% Part (a) Find the speed, in centimeters per second, of the shadow at t = 1/4 s.

Respuesta :

Answer:

The speed of the shadow is -193 cm/s.

Explanation:

Give that,

The x-coordinate of the shadow is given by the following function is given by :

[tex]x(t)=45\cos \pi t[/tex]

We need to find the speed of the shadow. The speed of particle in terms of displacement is given by :

[tex]v=\dfrac{dx}{dt}\\\\v=\dfrac{d(45\cos (\pi t))}{dt}\\\\v=-45\pi \sin (\pi t)\ ..........(1)[/tex]

At t = 1/4 seconds,

[tex]v=-45\pi \sin (\dfrac{\pi}{4})\\\\v=-1.93\ m/s\\\\v=-193\ cm/s[/tex]

So, the speed of the shadow is -193 cm/s.

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