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3 years ago

You are out running and the first mile takes you 10 minutes. The second mile takes you 20 minutes. This is an example of

1 answer:

5 0

If Equal distance is traveled in equal interval of time then it is known as uniform motion in which velocity of object will remain same.

Then if distance covered will be same and the time taken to cover same distance is decreasing then it shows that speed is increasing with time due to which it took less time to cover same distance. This is also known as positive acceleration.

Now if the distance covered will be same and time taken to cover same distance is increasing then it shows that speed is decreasing with time due to which it took more time to cover the same distance. This is also known as negative acceleration.

Now in the above case it is given that the first mile takes you 10 minutes. The second mile takes you 20 minutes. So the time taken is increasing while we cover same distance so this is an example of <u>Negative Acceleration</u>

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The function x = (1.2 m) cos[(3πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 9.7 s, what are the (a) di

nlexa [21]

Answer and Explanation:

Let:

$x(t)=Acos(\omega t+ \phi)$

The equation representing a simple harmonic motion, where:

$x=Displacement\hspace{3}from\hspace{3}the\hspace{3}equilibrium\hspace{3}point\\A=Amplitude \hspace{3}of\hspace{3} motion\\\omega= Angular \hspace{3}frequency\\\phi=Initial\hspace{3} phase\\t=time$

As you may know the derivative of the position is the velocity and the derivative of the velocity is the acceleration. So we can get the velocity and the acceleration by deriving the position:

$v(t)=\frac{dx(t)}{dt} =- \omega A sin(\omega t + \phi)\\\\a(t)=\frac{dv(t)}{dt} =- \omega^2 A cos(\omega t + \phi)$

Also, you may know these fundamental formulas:

$f=\frac{\omega}{2 \pi} \\\\T=\frac{2 \pi}{\omega}$

Now, using the previous information and the data provided by the problem, let's solve the questions:

(a)

$x(9.7)=1.2 cos((3 \pi *(9.7))+\frac{\pi}{5} ) \approx -0.70534m$

(b)

$v(9.7)=-(3\pi) (1.2) sin((3\pi *(9.7))+\frac{\pi}{5} ) \approx 9.1498 m/s$

(c)

$a(9.7)=-(3 \pi)^2(1.2)cos((3\pi*(9.7))+\frac{\pi}{5} )\approx -62.653m/s^2$

(d)

We can extract the phase of the motion, the angular frequency and the amplitude from the equation provided by the problem:

$\phi = \frac{\pi}{5}$

(e)

$f=\frac{\omega}{2 \pi} =\frac{3\pi}{2 \pi} =\frac{3}{2} =1.5 Hz$

(f)

$T=\frac{2 \pi}{\omega} =\frac{2 \pi}{3 \pi} =\frac{2}{3} \approx 0.667s$

8 0

3 years ago

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Which climate condition is typically found in the tropics due to the interaction of the atmosphere and hydrosphere?

Ilya [14]

The answer is A! Hope I helped!

7 0

3 years ago

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A cannon ball is shot straight upward with a velocity of 72.50 m/s. How high is the cannon ball above the ground 3.30 seconds af

disa [49]

Answer:

Explanation:

Given

Cannon is fired with a velocity of $u=72.50\ m/s$

Using Equation of motion

$y=ut+\frac{1}{2}at^2$

where

$y=displacement$

$u=initial\ velocity$

$a=acceleration$

$t=time$

after time $t=3.3 s$

$y=72.50\times 3.3-\frac{1}{2}\times 9.8\times (3.3)^2$

$y=239.25-53.36$

$y=185.89\ m$

So after 3.3 s cannon ball is at a height of 185.89 m

6 0

3 years ago

If you throw a baseball straight up,What is its velocity at the highest point?

sveta [45]

Answer: 52.

Explanation: Critical Thinking When a ball is thrown vertically up, it keeps going up until it hits a certain position, and then falls down. At the maximum point, the velocity is instantaneously zero.

I may or may not be a nerd lol.

Hope This Helps!!! : )

7 0

3 years ago

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A. What are the three longest wavelengths for standing waves on a 240-cm-long string that is fixed at both ends?

vovangra [49]

Answer:

a) the three longest wavelengths = 4.8m, 2.4m, 1.6m

b) what is the frequency of the third-longest wavelength = 75Hz

Explanation:

The steps and appropriate formula and substitution is as shown in the attached file.