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2 years ago

12

It takes 15 minutes to walk to the mall from your house at an average velocity of 1.1 m/s to the east. What is the displacement

from your house to the mall?

1 answer:

Anna11 [10]2 years ago

4 0

15 minutes = 15*60 = 900 seconds

900x1.1 = 990 m

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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

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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}$

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The iron nail’s mass is 16 grams and its temperature drops 650 C when dropped into the water. How much heat energy did the iron

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The heat energy transferred by the iron nail is 4680 J

Explanation:

The thermal energy transferred by a substance to another substance is given by the equation

$Q=mC\Delta T$

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C is its specific heat capacity

$\Delta T$ is its change in temperature

For the iron nail in this problem, we have:

m = 16 g

$C=0.450 J/g^{\circ}C$

$\Delta T = -650^{\circ}C$

So, the amount of heat energy given off by the nail is

$Q=(16)(0.450)(-650)=-4680 J$

where the negative sign indicates that the heat is given off.

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A failure of the red-sensitive nerves in the eye to respond to light properly causes

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<span>Color blindness is the failure of the red sensitive nerves in the eye that don't respond to light properly.</span>

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If the line is curved, the slope is changing, which also means the velocity is changing. In a distance-time graph, the gradient of the line is equal to the speed of the object. The more the gradient (and the steeper the line) the faster the object is moving.

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