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3 years ago

What is an independent variable ?

Physics

2 answers:

kkurt [141]3 years ago

7 0

<span>a variable whose variation does not depend on that of another.
</span>

seropon [69]3 years ago

6 0

An independent variable is a variable that does not depend on anything. It is manipulated to determine the value of a dependent variable<span>. The dependent variable is what is being measured in an experiment or evaluated in a mathematical equation and the independent variables are the inputs to that measurement. Example: Time would always be an independent variable because nothing affects time, however, time can affect everything. </span>

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A particle moves in a straight line with the velocity function v ( t ) = sin ( w t ) cos 3 ( w t ) . find its position function

Sunny_sXe [5.5K]

Integrating the velocity equation, we will see that the position equation is:

$$f(t)=\frac{\cos ^3(\omega t)-1}{3}$

<h3>How to get the position equation of the particle?</h3>

Let the velocity of the particle is:

$$v(t)=\sin (\omega t) * \cos ^2(\omega t)$

To get the position equation we just need to integrate the above equation:

$$f(t)=\int \sin (\omega t) * \cos ^2(\omega t) d t$

$$\mathrm{u}=\cos (\omega \mathrm{t})$

Then:

$$d u=-\sin (\omega t) d t$

$\Rightarrow d t=-d u / \sin (\omega t)$

Replacing that in our integral we get:

$\int \sin (\omega t) * \cos ^2(\omega t) d t$

$-\int \frac{\sin (\omega t) * u^2 d u}{\sin (\omega t)}-\int u^2 d t=-\frac{u^3}{3}+c$

Where C is a constant of integration.

Now we remember that $u=\cos (\omega t)$

Then we have:

$$f(t)=\frac{\cos ^3(\omega t)}{3}+C$

To find the value of C, we use the fact that f(0) = 0.

$$f(t)=\frac{\cos ^3(\omega * 0)}{3}+C=\frac{1}{3}+C=0$

C = -1 / 3

Then the position function is:

$$f(t)=\frac{\cos ^3(\omega t)-1}{3}$

Integrating the velocity equation, we will see that the position equation is:

$$f(t)=\frac{\cos ^3(\omega t)-1}{3}$

To learn more about motion equations, refer to:

brainly.com/question/19365526

#SPJ4

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If you could live any where except for where you are now where would you live

laila [671]

Answer:

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Explanation:

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3 years ago

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Ostrovityanka [42]

Burning of gases is one the example of chemical change

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3 years ago

He change in pitch due to a moving wave source is called ______.

Studentka2010 [4]

B) the Doppler effect

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2 years ago

A train travels 59 kilometers in 3 hours, and then 74 kilometers in 5 hours. What is its average speed?

dybincka [34]

Average speed = (total distance) / (total time)

Total distance = 59 km + 74 km = 133 km

Total time = 3 hrs + 5 hrs = 8 hrs

Average speed = (133 km) / (8 hrs) = 16.625 km/hr

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3 years ago