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3 years ago

I need help with this question really urgent

Physics

1 answer:

Verizon [17]3 years ago

5 0

Answer:

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3600.00

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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

4 0

1 year ago

An 4-kg ball experiences a force and accelerates at a rate of 1.5 m/s.

ANTONII [103]

Answer:

6.0 N

Explanation:

The strength of a force is expressed as the magnitude of the force in Newton.

The formula to apply here is :

Force= mass * acceleration

F=ma

Mass, m = 4 kg

Acceleration = 1.5 m/s²

Force= 4 *1.5 = 6.0 N

4 0

3 years ago

Which subatomic particle can be absent from an atom?

Alika [10]

Neutron can be absent

5 0

3 years ago

14. The resistance of dry human skin is about 500,000 ohms and wet,

Taya2010 [7]

Answer:

current is equal to V/R

Explanation:

I = 9/1000A

$9 \times 10 ^{ - 3}$

4 0

3 years ago

Use Hooke's Law to determine the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters.

ladessa [460]

Answer:

Work Done = 67.5 J

Explanation:

First we find the value of spring constant (k) using Hooke's Law. Hooke's is formulated as:

F = kx

where,

F = Force Applied = 450 N

k = Spring Constant = ?

x = Stretched Length = 30 cm = 0.3 m

Therefore,

450 N = k(0.3 m)

k = 450 N/0.3 m

k = 1500 N/m

Now, the formula for the work done in stretching the spring is given as:

W = (1/2)kx²

Where,

W = Work done = ?

k = 1500 N/m

x = 70 cm - 40 cm = 0.3 m

Therefore,

W = (1/2)(1500 N/m)(0.3 m)²

3 0

3 years ago