A particle's position (in meters) is given by the equation s(t) = 5x sin(2x), on the interval [-1, 4] minutes. What is its instantaneous velocity at t = 0?

Answers

Answer 1

You almost certainly meant to say the particle's position is a function of time t, not some other variable x (or vice versa) so that

s(t) = 5t sin(2t)

Differentiate s(t) to get the instantaneous velocity of the particle at time t. By the product rule,

s'(t) = 5 sin(2t) + 10t cos(2t)

Evaluate the derivative at t = 0 :

s'(0) = 0

Answer 2

The instantaneous velocity at t = 0 is 0 m/s.

To find the instantaneous velocity at t = 0, we need to take the derivative of the position function s(t) with respect to time (t). The derivative of s(t) gives us the velocity function v(t), which represents the particle's velocity at any given time t.

Given the position function s(t) = 5t * sin(2t), we find the velocity function v(t) by taking the derivative:

v(t) = d/dt (5t * sin(2t)).

To find the velocity at t = 0, we substitute t = 0 into the velocity function:

v(0) = 5 * 0 * sin(2 * 0) = 0.

Therefore, the instantaneous velocity of the particle at t = 0 is 0 m/s. This means that at t = 0, the particle is momentarily at rest, and its velocity is neither increasing nor decreasing at that specific moment.

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Related Questions

in this image of a series circuit, which light bulb will the current reach first

a. bulb a
b. bulb b
c. bulb c
d. a, b, and c simultaneously

Answers

I think the answer is D.

Explanation: Assuming that all the bulbs in a circuit are identical, incandescent-style ones, they will all light up at the same time.

If a typical house requires 235 W of electric power on average, how much deuterium fuel would have to be used in a year to supply these electrical needs

Answers

For a typical house requires 235 W of electric power on average,  deuterium fuel used is mathematically given as

E=79206.75

How much deuterium fuel would have to be used in a year to supply these electrical needs?

Generally, the mass and time statement  of deuterium is mathematically given as

Mass deuterium=2.014g

time =3.15*107s= 1year

In conclusion, energy

E=235*3.15*107s

E=79206.75

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What is best to say about a runner who is running at a constant velocity? a. their acceleration is positive. b. their acceleration is negative. c. their acceleration is zero. d. their acceleration cannot be determined. please select the best answer from the choices provided. a b c d

Answers

Answer:

C

Explanation:

because acceleration is the rate of change of velocity.

Answer:

C

Explanation:

bcuz i said its c cuzzo

As a general rule, what will create greater drag on an object?

Answers

Answer:

the faster you move the greater, the drag force acting against the object.

Explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

The faster you move the more force will drag

The electronic circuitry in an ultrasonic receiver measures the transit time and calculates the distance from the receiver to the surface of material.
a. True
b. False

Answers

Answer: False

Explanation:

The half life of uranium-235 is 4. 5 billion years. If 0. 5 half-lives have elapsed, how many years have gone by?


a. 9 billion

b. 2. 25 billion

c. 4. 50 billion

d. 4. 0 billion

Answers

Answer:

2.25 billion years

Explanation:

i am smort

You throw a 0.5 kg ball with a force of 10 N. What is the acceleration of the ball?

Answers

Answer:

20m/s^2

Explanation:

F=ma, therefore 10N = 0.5kg * a. Solve for a.

What does sound travel through?

Answers

Answer:

Solids liquids and gases

Explanation:

sound will not travel in a vacuum

An electric appliance is connected by wires to a 240-volt source of voltage. If the combined resistance of the appliance and wires is 12 ohms, how much current is flowing through the circuit?

Answers

Voltage=V=240VResistance=R=12ohmCurrent be I

Apply ohms law

V=IR240=12II=240/12I=20A

Answer :-

Current is 20 Ampere .

Explanation :-

As per the provided information in the given question, we have been given that the Potential Difference is 240 Volt's . Resistance is given as 12 Ohm's . And, we have been asked to calculate the Current .

For calculating the Current , we will use the Formula :-

[tex] \bigstar \: \: \: \boxed{ \sf{ \: Current \: = \: \dfrac{Voltage}{Resistance} \: }} \\ [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \Longrightarrow \: \: \: \sf { Current \: = \: \dfrac{Voltage}{Resistance} } \\ [/tex]

[tex] \Longrightarrow \: \: \: \sf { Current \: = \: \dfrac{ \: 240 \: }{12} } \\ [/tex]

[tex] \Longrightarrow \: \: \textbf {\textsf { Current \: = \: 20 }} \\ [/tex]

Hence :-

Current = 20 Ampere .

[tex] \underline {\rule {180pt}{4pt}} [/tex]

Additional Information :-

[tex] \Longrightarrow \: \: \: \sf {Voltage \: = \: Current \: \times \: Resistance} [/tex]

[tex] \Longrightarrow \: \: \: \sf {Current \: = \: \dfrac {Voltage}{Resistance} } [/tex]

[tex] \Longrightarrow \: \: \: \sf {Resistance \: = \: \dfrac {Voltage}{Current} } [/tex]


How fast does an X-ray travel through space?

Answers

Answer:

As with other forms of electromagnetic radiation, X-rays can be described as coupled waves of electric and magnetic fields traveling at the speed of light (about 300,000 km, or 186,000 miles, per second).

Explanation:

hope it's help

According to Newton's Law of Gravity, if two objects were to move twice as far apart, the force of gravity between them would be...

Answers

The force of gravity between them given the data from the question, would decrease by a factor of 4

Newton's law of gravity

F = GM₁M₂ / r²

Where

F is the force G is the gravitational constant M₁ and M₂ are the masses of the objectsr is the distance apart

Data obtained from the question Initial distance apart (r₁) =  rInitial force (F₁) = FFinal distance apart (r₂) = 2rFinal force (F₂) =?

How to determine the final force

F = GM₁M₂ / r²

Cross multiply

Fr² = GM₁M₂

GM₁M₂ = constant

F₁r₁² = F₂r₂²

With the above formula, we can obtain the final force as follow:

F₁r₁² = F₂r₂²

F × r² = F₂ × (2r)²

Fr² = F₂ × 4r²

Divide both side by 4r²

F₂ = Fr² / 4r²

F₂ = F / 4

Thus, we can conclude that the final force will decrease by a factor of 4

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Voltage ___ commonly occur when large loads, such as motors, are turned off and voltage on the power line increases above the normal voltage fluctuation (+10%) for a short period of time.

Answers

Answer:

Voltage SPIKES

Explanation:

Continental air masses usually contain less moisture because they...


...originate over water.


...originate over ice.


...move from water onto land.


...originate over land.

brainliest for correct answer

Answers

Answer:

I believe its either the 3rd or 4th one

Explanation:

I'm not sure if these are correct sorry if this is a false or unhelpful anwser

2.
What is the coefficient of friction between a block of wood that weighs 12.2
N and requires a force of 2 N to pull along at a constant velocity?
Want
Equation and solve
Given

Answers

Answer:

0.163934

Explanation:

Kinetic friction can be calculated by coefficient of kinetic friction * normal force. In this question the Mg is = to normal force (12.2 N). Therefore using sum of forces equations we get 2N = coefficient of kinetic friction * 12.2N. divide 2 by 12.2 to get the coefficient.

What is the current in a bulb if the resistance of its filament is 2 ohms and it is connected across a 6-volt battery

Answers

Answer:

3 amps

Explanation:

V = IR

6 = I * 2

I = 3 amps

downhill water movement is responsible for

Answers

Current from water being moved down

Seeds are often found on which part of a gymnosperm?

branch
leaf
cone
stem

Answers

Answer: Cone



Explanation: gymnosperm, any vascular plant that reproduces by means of an exposed seed—unlike angiosperms, or flowering plants, whose seeds are enclosed by mature fruits. The seeds of many gymnosperms (literally, “n4ked seeds”) are borne in cones and are not visible until maturity.

A light bulb has a resistance of 360 . What is the current in the bulb when it has a potential difference of 120 V across it?

0.33 A
3 A
480 A
43,200 A

Answers

Answer:

333 mAmps      .33 A

Explanation:

v = ir

v/r = i

120 v / 360 ohm = .3333 A

Answer:

A). 0.33A

Explanation:

If new evidence is discovered that a theory does not accommodateoptions:

the theory is disproved and thrown out


the theory then becomes a law


the theory is generally modified in light of this new evidence


the theory can not change so it stays the same

Answers

Answer:

The theory is generally modified in light of this new evidence.

explain how to identify the points under compression and tension ​

Answers

Answer:

Pls make me brainliest

Explanation:

the compression force is the force generated from compressing an object or substance. When shearing forces are aligned into each other, they are called compression forces.

The compression force is used to power everything from compression brakes to hand tools. The compressive strength of materials and structures is an important engineering consideration.

The compression force can be visualized by placing an object on a spring. When the spring is compressed and then released, the object is ejected into the air.

This is a result of the compression force that is generated from compressing the spring.

This system has a constant velocity, and there is an equilibrium because the tension in the cable, which is pulling up the object, is equal to the weight force, i.e., mg. Where M is a mass, and g is the acceleration caused by gravity, which is pulling down the object.

The Formula of Tension.

T = Mg

Tension word becomes from a Latin word meaning “to stretch.” Testing part of the force, Like one type of pull force. All physical objects that are in contact may exert forces on each other.

This contact forces different names based on these types of objects in contact. Where one of the objects exerting the force happens to be a rope, string, chain, or cable we call the force tensions

The potential difference across a conducior is 6.0V. What is the energy dissipaled when a current of 5.0 A flows for 1 minute?

Answers

Answer:

1/2 watt hr    

Explanation:

watts = V I   =   6 * 5 = 30 watts   for 1/60 hr

30 watts * 1/60 hr = 1/2  watt hr

Can electromagnetic waves travel in a vacuum?

Yes
Or
No

Answers

Answer:

Yes

Explanation:

Yes because Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.

2 ton car that starts from rest under the action of traction engine for 30 seconds gains speed 52 km / h. the coefficient of friction between the wheels of the car and the road is 0.02. find: the work done by the traction of the engine and the friction beam on the car at this time​

Answers

Answer:

1 m/s=3.6km/her

56km/hr=?

=56km/hr×1m/s/3.6km/her

velocity is 15.5m/s

Explanation:

w=fs

a=v/t

a=15.5m/s/30s

a=465m/s^2

w=fs

w=0.02×

The spring of a dart gun exerts a force on a 0.02 kg dart as it is launched from the gun with 4.00 J of KE. At what velocity does the dart come out of the gun?

Answers

Let's see

KE=1/2mv²

m is mass and v is velocity

2KE=mv²4(2)=0.02v²8=2v²/1002v²=800v²=400v=20m/s

If you pull a permanent magnet rapidly away from a tank circuit, what is likely to happen in that circuit?.

Answers

Answer:

attract the magnetic ratio engine light of rock level

Starting from rest, an object accelerates on a straight level surface at the rate of 2 m/s for 10 s. 9. What is the speed of the object at the end of 10 s? (A)5 m/s (B) 10 m/s (C) 20 m/s (D) 30 m/s (E) 40 m/s​

Answers

Answer:

C

Explanation:

a = v-u / t

a×t = v (u= 0 therefore is ignored)

2m/s² × 10s = v

v= 20m/s

Based on the information in the table, choose whether the magnetic field is weak or strong
Current Number of Coils Magnetic Field Strength 0. 2 A Many _______________
5. 0 A Many _______________
5. 0 A Few _______________
put weak or strong in the blanks

Answers

Answer:

Explanation:

Field characteristics

The strength of the field at the Earth's surface ranges from less than 30 microteslas (0.3 gauss) in an area including most of South America and South Africa to over 60 microteslas (0.6 gauss) around the magnetic poles in northern Canada and south of Australia, and in part of Siberia.

Marcus plucks at an outstretched coil and observes the following wave motion. what is the motion of the particles in this kind of wave? a hand holds the left end of a set of waves. the wave has longer and shorter spaces between successive waves as it spreads to the right. a label wave motion is above the series of waves and an arrow next to the label points right. the particles will move up and down over large areas. the particles will move up and down over small areas. the particles will move side to side over small areas. the particles will move side to side over large areas.

Answers

The motion of the particles in this kind of wave will be option C that is The particles will move side to side over small areas.

What is a wave?

A wave can be described as a disturbance that travels through a medium from one location to another location.

When Marcus plucks an outstretched coil, the coli sets into wave like motion that is oscillates to and fro. The particles of the medium do not move along the wave but just vibrate sideways about a fixed position.

The particles would move side to side over very small areas. Such type of wave is known as a mechanical wave. A Sound wave is a mechanical wave.

The particles vibrate in the direction of the motion of the wave. The wave carries forward the energy.

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Answer:

C is the correct answer. :)

Explanation:

A 160 kg cart has a momentum of 870 kg m/s. What is the velocity of the cart?

Answers

Answer: 5.44 m/s

Explanation:

Given:

Mass of cart: 160 kg

Momentum of cart: 870 kg•m/s

[tex]$$Momentum $|\rho|=m \times v$$$\begin{aligned}&870 \ kg\cdot m/s=160 \mathrm{~kg} \times v \\&v=5.44 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]

Answer:

The momentum is defined as :

P=mv

Where m is the mass and v is the velocity. In this case we know the mass is 160 kg and the momentum is 870 kg plugging in this equation above and solving for the velocity we have

870=160V

V=870÷160

V=5.44

Therefore, the velocity of the cart is 5.44 m/s.

PLEASE HELP: Do you think there could be another period of time when so many brilliant discoveries are made in such a span of time? Why or Why not? Make sure to research other times to be able to defend your point.

Answers

Answer:

"Emerging technologies, such as industrial robots, artificial intelligence, and machine learning, are advancing at a rapid pace. These developments can improve the speed, quality, and cost of goods and services, but they also displace large numbers of workers."

Explanation:

This means in the furture we will have many technologies doing our day to day life things.

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