If Joe rides south on his bicycle in a straight line for 15 min with a average speed of 12.5 Km/h, how far has he ridden?

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

2 years ago

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A carmaker has designed a car that can reach a maximum acceleration of 12 meters per second the cars mass is 1515 assuming the s

Rudiy27

The answer is attached. Also, you should know that the unit for acceleration is m/s2 and for velocity it is m/s.

5 0

3 years ago

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Q is granite, an igneous rock. Which of these is NOT a characteristic of igneous rock?

fgiga [73]

Igneous rocks are conglomerates, predominantly composed of rounded

gravel

Explanation:

The statement that igneous rocks are conglomerate predominantly composed of rounded gravel is not correct. Igneous rocks are rocks formed from magma that cools and solidifies.

Conglomerates are sedimentary rocks that are made of rounded clasts in a matrix.
They differ from igneous rocks that crystallize from molten magma.
Sedimentary rocks are usually derived from the process of weathering, erosion, transportation and deposition on the earth surface.
Igneous rocks forms from crystallized magma which can be on the surface or deep within the crust.

Learn more:

Sedimentary rocks brainly.com/question/2740663

#learnwithBrainly

8 0

2 years ago

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What is the correct definition of nurture?

makkiz [27]

Answer:

(C) the fulfillment of physical, mental, emotional, and social needs

Explanation:

Nurture