The displacement of an object in SHM is described by the equation
[tex] x = cos\binom{2\pi}{3}t[/tex]
where x is in meters and t in seconds. Determine the velocity of the object at t = 0.6 s. ​

Answers

Answer 1

Answer:

[tex]-1.99\:\mathrm{m/s}[/tex]

Explanation:

Assuming that the equation is intended to be [tex]\displaystyle x=\cos\left(\frac{2\pi}{3}t\right)[/tex], we can find the velocity vs. time equation by taking the first derivative with respect to [tex]t[/tex]:

[tex]\displaystyle \frac{dx}{dt}=\frac{d}{dt}\left(\cos\left(\frac{2\pi}{3}t\right)\right)[/tex]

Recall the chain rule:

[tex]\displaystyle f(g(x))'=f'(g(x))\cdot g'(x)[/tex]

Therefore,

[tex]\displaystyle \frac{d}{dt}\left(\cos\left(\frac{2\pi}{3}t\right)\right)=-\sin\left(\frac{2\pi}{3}t\right)\cdot \frac{2\pi}{3}[/tex]

Therefore, the velocity vs. time equation of the object is [tex]\displaystyle v=-\sin\left(\frac{2\pi}{3}t\right)\cdot \frac{2\pi}{3}[/tex].

Substitute [tex]t=0.6\text{ s}[/tex] into this equation to find the velocity at that given time:

[tex]\displaystyle v=-\sin\left(\frac{2\pi}{3}(0.6)\right)\cdot \frac{2\pi}{3}\approx \boxed{-1.99\text{ m/s}}[/tex]


Related Questions

Name the type of joint present in skull.​

Answers

Answer:

Sutures are nonmoving joints that connect bones of the skull

Explanation:

These joints have serrated edges that lock together with fibers of connective tissue.

Answer:

Immovable fibrous joints are present in our skull

Explanation:

brainliest plz

A bowling ball, basketball, and tennis ball are all raised to the same height above the ground. Give the order of objects from the least potential energy to the most

Answers

Answer:

bowling ball, basket ball, tennis ball

Explanation:

Once you start pulling your object with less force than friction, what should you expect your object to do? What about when your object is pulled with more force than friction?
NO LINK S​

Answers

#Case -1

If Pulling force is less than frictional force the object won't move .

#Case-2

If Pulling force is greater than frictional force then object will be .

In order to calculate friction force you need Limiting friction first .

[tex]\\ \sf\longmapsto F_L=\mu sN[/tex]

u s is coefficient of static friction and N is normal reaction

Or

[tex]\\ \sf\longmapsto F_L=\mu smg[/tex]

As N=mg

1. What does the term monecious mean?

Answers

Answer:

Monecious is a plant or invertebrate animal having both the male and female reproductive organs in the same individual; hermaphrodite.

If you traveled 50m/s for 60 seconds, how far did you travel? Remember speed=distance/time
Question options:


300 m/s



500 m/s



3,000 m/s



300 km/h

for some reason my question got removed-_-

Answers

the answer is 3,000 m/s

In hockey activities, a warm hockey puck and a frozen hockey puck has a different coefficient of restitution: 0.5 for a warm hockey puck, and 0.35 for a frozen one. NHL requires the frozen pucks to be used in games. To make sure the puck can be used in the game, the referee drops the puck on its side from a height of 2.5 m. How high should the puck bounce if it is a frozen puck

Answers

If its is a frozen hockey puck, it bounce off the ground after collision to a height of 0.3m.

Given the data in the question;

Since the hockey puck was initially in the referee's hands

Initial velocity; [tex]u = 0m/s[/tex]Distance or height from which it was dropped;  [tex]h = 2.5m[/tex]Acceleration due to gravity; [tex]g = 9.8 m/s^2[/tex]Coefficient of restitution a frozen puck; [tex]0.35[/tex]

First we will find the velocity of the Puck when it hits the ground

From the Third Equation of Motion:

[tex]v^2 = u^2 + 2as[/tex]

Where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity and s is the distance.

Since the pluck is under gravity, we will have:

[tex]v^2 = u^2 + 2gh[/tex]

We substitute in our value and find "v"

[tex]v^2 = 0 + (2 \ *\ 9.8m/s^2\ *\ 2.5m )\\\\v^2 = 47.04m^2/s^2\\\\v= \sqrt{47.04m^2/s^2}\\\\v = 6.85857m/s[/tex]

Now, Velocity of the hock puck after it hits the ground and bounce back;

We know that; Coefficient of restitution [tex]= \frac{Relative\ velocity\ after\ collision}{Relative\ velocity\ before\ collision}[/tex]

Hence, Relative Velocity after collision = Coefficient of restitution × Relative Velocity before collision

we substitute in our values;

Relative Velocity after collision [tex]= 0.35 \ *\ 6.85857m/s[/tex]

Relative Velocity after collision [tex]= 2.4 m/s[/tex]

Now, to determine how high should the puck bounced back

We use the Third Equation of Motion:

[tex]v^2 = u^2 + 2as[/tex]

Where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity and s is the distance.

Since the pluck is under gravity, we will have:

[tex]v^2 = u^2 + 2gh[/tex]

Now, since the hockey puck bounces back, it is experiencing a negative acceleration

Hence, the equation becomes

[tex]v^2 = u^2 - 2gh[/tex]

We substitute our values into the equation and find "h"

[tex](0m/s)^2 = (2.4m/s)^2 - ( 2*9.8m/s^2*h)\\\\0 = 5.76m^2/s^2 - (19.6m/s^2*h)\\\\(19.6m/s*h) = 5.76m^2/s^2 \\\\h= \frac{ 5.76m^2/s^2 }{19.6m/s^2}\\\\h = 0.3m[/tex]

Therefore, If its is a frozen hockey puck, it bounce off the ground after collision to a height of 0.3m.

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THE BEST ANSWER WILL BE MARKED THE BRAINLIEST!

While driving your car at a fast constant speed, you have to press down hard on your gas pedal than you do while driving at a slower constant speed.

In both cases, the net force on your car is zero. Explain why you have to apply a greater pressure to your gas pedal.

Answers

Answer:

You have to apply more pressure to the pedal so more gas runs through the car allowing it to reach higher speeds

To move, a car or any other object must be accelerated from rest to the desired speed; this necessitates that the engine force be greater than the friction force. The net force must be zero once the car is moving at constant velocity; otherwise, the car will accelerate (gain speed).

What forces act on a car at constant speed?All forces acting on a car moving at a constant speed (uniform motion) are balanced. In this case, the two opposing backward forces (air resistance and friction) perfectly balance the applied force of the wheels on the road.When we say constant speed, we mean that a body or object moves at a constant change in distance over time. For example, if we are walking in a straight line at 1 step per second, we can say we are moving at a constant speed. Our acceleration is equal to zero in this case.

To learn more about : Speed

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#SPJ2

You throw a rock up into the air as hard as you can. It stays in the air a total of 6.0 s. What
was the velocity of the rock when you threw it?

Answers

Answer:

5.9 x 10

Explanation:

What is sustainability? How can we make sustainable development a reality? How sustainability can be measured?​

Answers

Answer:

1)The ability to be maintained at a certain rate or amount is called sustainability.

3)Sustainability is measured by assessing performance of Social, Environmental, and Economic principles.

sorry but I don't know number 2.

I hope it will help you)):

Ano ang mangyayari kung hindi mo gagamitin ang iyong talento?​

Answers

Answer:

mas lalo kang tinatamaran magaral

25. Which of the following cannot be broken down into smaller parts through ordinary chemical means?
a. Nitrogen
b. Protein
C. Salt
d. Sugar

Answers

Answer:

the correct answer is sugar

I think it’s Sugar!!!!!

Jonathan wants to separate stones, insects and other unwanted materials in his mixture of grains and corn. What technique of separating mixture is appropriate

A. Winnowing
B. physical manipulation
C. Filtering
D. Magnetism​

Answers

Answer:

What is B physical manipulation

Explanation:

Physical manipulation means fertilizers that are manufactured, blended, or mixed, or animal manures or compost that have been changed from their initial physical state by manipulations such as drying, cooking, chopping, grinding, shredding, ashing, or pelleting.

Please allow me to know if my answer helped you with a thank you!

Miss Hawaii

How can wind, coiled wire, and magnets be used together to generate electricity?

Answers

Answer:

b

Explanation:

hope helpful

have a great day

Speed depends on how far something travels and

Answers

Answer:

Speed depends on how far something is travelling and the time taken for the object to travel that distance

Explanation:

(In reference to the speed formula)  Speed=[tex]\frac{Distance(m)}{Time(m/s)}[/tex]

Definition of speed:

Speed is the magnitude (unit) of the rate at which an object is moving.

(pls do correct me if I have any mistakes it makes a big difference to help each other out!)

The gravitational force between two objects is 2700 N. What will be the gravitational force between the objects if the distance between them triples?

Answers

F = GMm/r^2

So F is proportional to 1/r^2

F2 = 2700 x ( 1 / 3^2 ) = 300N

As two objects are separated from each other, the force of gravitational attraction between them also decreases. ... If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

Which of the following statements is true?
a Penicillin is produced by fungal fermentation.
b
The effects of too much beer or wine can be
countered with antibiotics.
с
The deadly Death Cap mushroom can be treated
with penicillin.
d Antibiotics do not treat fungal diseases.

Answers

Answer:

a Penicillin is produced by fungal fermentation.

Explanation:

The industrial production of penicillin (PEN) occurs via fermentation using the filamentous fungus Penicillium chrysogenum

Penicillin G (benzylpenicillin) was first produced from a penicillium fungus that occurs in nature. The strain of fungus used today for the manufacture of penicillin G was created by genetic engineering to improve the yield in the manufacturing process.

Motion maps for two objects, Y & Z, are shown.

How many seconds does Object Z start before Object Y?
- 2
- 3
- 4
- 5

Answers

Answer: it’s 3 seconds

Explanation:

Answer:

B

Explanation:

3 seconds, hope it helps

Two horses are side by side on a carousel. Which has a greater tangential speed the one closer to the center or the one farther from the center? Explain your answer.​

Answers

Answer:

The horse father from the center has a greater tangential speed. Although both horses complete one circle in the same time period, the one farther from the center covers a greater distance during that same period.

Explanation:

find charge and charge density on the surface of a conducting sphere of radius 15.2cm where potential at 215 v

Answers

this is the correct answer

describe an experiment to demonstrate surface tension in a liquid​

Answers

Answer:

mę břöőda I dunno this answer

Explanation:

hope you find it

Surface Tension in a Liquid

Materials for Experiment

cereal bowl water ground black pepper liquid soap a toothpick

Procedure for Experiment

Fill a bowl with water Shake the black pepper onto the surface of the water (Notice how it stays afloat on the water? That is the surface tension holding the layer up) Take a toothpick and put the end into soap so that it coats the end Gently touch the surface of the water with the toothpick Did you see how the pepper shoots back in all directions? What must the soap be doing to the surface tension? Soap is something that actually breaks down the cohesive powers of water, making it have less surface tension. If you mix some soap with water and make a water droplet on your counter again, what do you think the shape would look like? Give it a try!

What is the magnitude of the electric field at a point 0.0075 m from a 0.0035
C charge?
Use E-
kq
and k - 9.00 x 10° N.m²/C2.
A. 1.9 x 1010 N
B. 4.2 x 10' N
O c. 5.6 x 1011 N
D. 5.5 x 1012 N

Answers

Explanation:

E = 9×10^9 × 0.0035 /(0.0075)²

= 9×10^9 × 3.5×10`³/(7.5×10`³)²

= 31.5×10^6 /(56.25 ×10^-6)

= 0.56 × 10^12

= 5.6 × 10^11 N/C (option C)

PLEASE HELP ASAP WILL GIVE BRAINLIEST ​

Answers

Explanation

(m) is measured in kilograms (kg)

(F) is measured in newtons (N)

acceleration (a) is measured in metres per second squared (m/s²)

Q1) ~mass (m) is measured in kilograms (kg) 

Q2)~acceleration (a) is measured in metres per second squared (m/s²)

Q3)~force (F) is measured in newtons (N)

Hope this helped you- have a good day bro cya)

Which theory of emotion explains the startle response

Answers

Answer:

In the present study, the startle blink reflex is used as a measure of emotion regulation to effective picture stimuli. Based on the aphasic theory of emotion, it is hypothesized that the startle response will be largest in magnitude in the presence of negative emotional stimuli (Varanasi, Spence, & Lang, 1988).

An object starts from rest and uniformly accelerates at a rate of 1.25 m/s2 for 7.0 seconds.
(a) What is the object's displacement during this 7-second time period?
(b) What is the object's final velocity?
(c) How many seconds does it take the object to have a displacement of 22 meters?

Answers

Explanation:

Since its accelerating, the velocity vs time graph is linear

For displacement we need initial velocity (which is zero because it starts from rest) and final velocity (which is calculatee thro acceleration formula

A= (vf - vi)/t

a= vf-0/t

1.25=vf / 7

1.25*7=vf

8.75 = vf

Now for displacement plug all the values in

X = 1/2(vf-vi)/t formula

The displacement (x) is 30.625 m

For part 3, we know new displacement that is 22m , the final and initial velocities are the same so just plug in the values for same formula above

The answer is t = 5.02

Im pretty sure all the answers are correct

A 10 kg box initially at a speed of 10 m/s accelerates uniformly to a speed of 20 m/s in 2
seconds. Determine the
A. energy gained by the block

Answers

Answer:

What Um Sorry Where's The Answer?....

How can people reconcile technology with environmental preservation?​

Answers

1. Developing renewable energy technology

- Efficient energy storage and smarter grids .
- renewable and rechargeable batteries and fuel cell

2. Saving endangered wildlife

-smart collars for endangered species and reducing human - animal conflict
-Gene sequencing for detecting and researching on deadly animal diseases.

3. Adopting a smarter lifestyle

- smart homes that promote energy saving and green - living .
- electric cars which are three times more conventional vehicles .

Hope this helps :)

help pls will give brainiest :)

Answers

Answer:

use a flight sim

12. Suppose the polar bears were running on land instead of swimming. if the polar bear runs
at a speed of about 5.5m/s how far will it travel in 55 seconds?

Answers

the polar bear will travel 302.5m

A stimulus that increses the occurance of a response is called

Answers

Answer:

reinforcing stimulus

Explanation:

Think its correct

Answer:

reinforcing stimulus

Explanation:

because it increases the occurence of a response

An object of mass 1.0 kg is at rest on a smooth inclined plane with height h, length 8 m,
and which makes an angle of 30° with the horizontal. The object is allowed to move, it
slides down and onto a rough horizontal surface. After traveling a distance of 4 m it hits a spring and travels 1.3 m more, all along the rough horizontal surface. The spring
constant is 26.5 N/m. What is the coefficient of kinetic friction for the horizontal surface?

Answers

The coefficient of kinetic friction for the rough horizontal surface is 0.66.

The given parameters;

mass of the object, m = 1 kglength of the inclined plane, L = 8 mangle of inclination of the plane, θ = 30⁰ distance traveled before hitting the spring, d₁ = 4 mdistance traveled after hitting the spring, d₂ = 1.3 mthe spring constant, k = 26.5 N/m

Apply work-energy theorem; the work done the force of friction is equal to the energy stored in the spring.

[tex]F_kd_1 = \frac{1}{2} kd_2^2\\\\\mu_kmg cos(\theta)d_1 = \frac{1}{2} kd_2^2\\\\\mu_k(1 \times 9.8 \times cos(30)\times 4) = \frac{1}{2} \times 26.5 \times (1.3)^2\\\\33.95\mu_k = 22.39\\\\\mu_k = \frac{22.39}{33.95} \\\\\mu_k = 0.66[/tex]

Thus, the coefficient of kinetic friction for the rough horizontal surface is 0.66.

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