Which indicates arson - (pick 2) v shaped burn, multiple point of origin, U shaped burn pattern, pour pattern

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

A 35kg cannonball sits at rest on a flat level surface. What is the normal force exerted on the cannon ball. Use -9.8 m/s2 for a

Tom [10]

Answer:

a) N = 343 [N]

Explanation:

We must remember Newton's third law, which tells us that the force acting on a body is equal to the normal reaction force of equal magnitude but acting in the opposite direction.

$N=m*g$

where:

m = mass = 35 [kg]

g = gravity acceleration = 9.81 [m/s²]

$N = 35*9.8\\N= 343 [N]$

8 0

2 years ago

QUICK!!!!! QUESTION ATTACHED!!!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!

Molodets [167]

Answer:

A works to find magnitude. The leading negative sign gives us the positive magnitude after the correct velocity is found without it.

8 0

3 years ago

What are the effects of forces to the motion of an object?

melamori03 [73]

Forces affect how objects move. They may cause motion; they may also slow, stop, or change the direction of motion of an object that is already moving. Since force cause changes in the speed or direction of an object, we can say that forces cause changes in velocity. Remember that acceleration is a change in velocity.

3 0

3 years ago

A 100 kg box as showsn above is being pulled along the x axis by a student. the box slides across a rough surface, and its posit

Anit [1.1K]

Answer:

a) 2 m/s

b) i) $K.E = 50 (1.5t^2 + 2) ^2\\$