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The position vector is given by vector r= 5t² I cap + 2 t³ j cap + 2 k cap. Find it's velocity and acceleration at t=2s.

Answers

Answer 1

Answer:

We have the position vector given in terms of time t. r(t) = t^3*i + t^2*j

To find the velocity vector we have to differentiate r(t) with respect to time.

r'(t) = 3t^2*i + 2t*j

The vector representing acceleration is the derivative of the position vector

r''(t) = 6t*i + 2*j

When time t = 2.

The velocity vector is 3*2^2*i + 2*2*j

=> 12*i + 4*j

The speed is the absolute value of the velocity vector or sqrt(12^2 + 4^2) = sqrt (144 + 16) = sqrt 160

The acceleration vector is 6*2*i + 2*j

=> 12*i + 2*j

The required acceleration at t=2 is 12*i + 2*j and the speed is sqrt 160.

Explanation:

Can I have thx and brainliest?

Answer 2
This is the written answers to find the velocity and acceleration of r
Will Mark As BRAINLIEST.......The Position Vector Is Given By Vector R= 5t I Cap + 2 T J Cap + 2 K Cap.

Related Questions


What is the speed of a cheetah that travels 176.4 meters in 4.5 seconds?

Answers

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{39.2 \: m/ {s} \: }}}}[/tex]

Explanation:

Given,

Distance travelled ( d ) = 176.4 meters

Time taken ( t ) = 4.5 seconds

Finding the speed of a cheetah

Speed [tex] \sf{ = \frac{distance \: travelled}{time \: taken} }[/tex]

[tex] \sf{ = \frac{176.4}{4.5} }[/tex]

[tex] \sf{ = 39.2 \: m/ {s} \: }[/tex]

------------------------------------------------------------------------

Let's learn about Speed :

Suppose a body moves 20 m in 2 seconds, either on a curved path or on a straight path. So , 10 m is the distance travelled by the body in each second which can be written as 10 m/s. This is called speed of the body. Thus, Speed is defined as the distance travelled per unit time. It is the rate of distance travelled by a body.

Mathematically,

[tex] \boxed{ \bold{ \sf{speed = \frac{distance \: travelled}{time \: taken} }}}[/tex]

In SI system, the unit of distance is metre and time is second. Thus , the SI unit is speed is m/s.

Hope I helped!

Best regards!!

A student uses a spring scale attached to a textbook to compare the static and kinetic friction between the textbook and the top of a lab table. If the scale measures 1,580 g while the student is pulling the sliding book along the table, which reading on the scale could have been possible at the moment the student overcame the static friction?

Answers

Answer:1860g

Explanation:The force would have to be greater than 1580g, which is when the student is pulling the sliding book with the spring scale

Jaiden is writing a report about the structure of the atom in her report,she says that the atom has three main parts and two subatomic particles. Do you agree with her?why or why not

Answers

Answer:

I do not agree with the answer.

Because in reality, the atom has 2 main parts and 3 subatomic particles.

Explanation:

The parts of an atom are:

- The crust: It is the outer part of the atom and is the place where the electrons are.

- The nucleus: It is the central part of the atom and is the place that contains the protons and neutrons.

The subatomic particles of the atom are:

- Electrons: They are negatively charged particles that go in the atom's crust and are divided into specific sections.

- Protons: They are particles with a positive electric charge, the number of protons in the nucleus of an atom is what determines the atomic number of an element.

- Neutrons: They are atoms with no electric charge.

How do we aquire knowledge in science?

Answers

Answer:

By studying.

By paying attention to what the teacher is saying.

That's the way to receive knowledge.

HAVE A GREAT DAY

Explanation:

Please give me that little crown...

AND REMEMBER TO SMILE

It takes Serina 1.72 hours to drive to school. Her route is 47 km long. What is Serina's average speed on her drive to school? Your Answer :

Answers

Explanation:

Average speed = distance / time

v_avg = 47 km / 1.72 hr

v_avg = 27.3 km/hr

Using a fixed 20 V from the power source and three lightbulbs that have the same resistance, how would you design a circuit that would allow at least one bulb to use maximum power (have maximum brightness)?

Answers

Answer:

check photo

Explanation:

We should connect the three bulbs in parallel in order to allow at least one bulb to use maximum power.

We have a 20 V power source and three lightbulbs that have the same resistance.

We have to design a circuit that would allow at least one bulb to use maximum power.

What is the total resistance of the circuit if three resistances each of of resistance R(1), R(2) and R(3) are connected in parallel ?

For parallel combination of resistances, the total resistance will be -

[tex]\frac{1}{R_{T} } =\frac{1}{R(1)} +\frac{1}{R(2)} +\frac{1}{R(3)} \\[/tex]

We know that the power dissipated by the resistance is equal to -

P = V x I = [tex]I^{2} R[/tex] = [tex]\frac{V^{2} }{R}[/tex]

Let the three bulbs be B(1), B(2) and B(3) each with resistance ' R '. In parallel combination of the bulbs, the voltage across each bulb will be same as that of power source -

V [B(1)] = V [B(2)] = V [B(3)] = 20 V

Therefore, the power used by each bulb will be -

P [B(1)] = P [B(2)] = P [B(3)]  = [tex]\frac{20\times 20}{R}=\frac{400}{R}[/tex]

Whereas, in series combination the voltage drop will regularly take place after the current passes through a resistor.

Hence, we should connect the three bulbs in parallel in order to allow at least one bulb to use maximum power.

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Brandon buys a new seadoo he goes 12 km north from the beach he jumps wakes for 6 km to the east the chases a boat 10 km north what distance did he cover what was his displacement

Answers

Answer:

Distance covered 28 km

displacement is 22.8 km North-East

Explanation:

Distance shows how far apart objects or points are from each other. The distance he covered is the sum of all the distance travelled. Therefore:

Distance covered = 12 km + 6 km + 10 km = 28 km

Displacement is a vector quantity (has direction). It is the overall change in position.

The total distance traveled north = 12 km + 10 km = 22 km

The distance traveled east = 6 km

The displacement (d) is:

d² = 22² + 6² = 484 + 36

d² = 520

d = √520 = 22.8 km

Therefore the displacement is 22.8 km North-East

Distance covered 28 km

displacement is 22.8 km North-East

The calculation is as follows:

Distance covered

= 12 km + 6 km + 10 km

= 28 km

Now

The total distance traveled north = 12 km + 10 km = 22 km

And,  

The distance traveled east = 6 km

So,  

The displacement (d) is:

[tex]d^2 = 22^2 + 6^2\\\\ d^2 = 520\\\\d = \sqrt520[/tex]

= 22.8 km

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the value of g is more in the poles of the earth,why?

Answers

Answer:

Explanation:

beacuse the poles are the cause of graIt's due to the rotation of earth about its own axis. Due to the rotation, objects placed on the surface of earth also rotates . Their rotational kinetic energy prevents them from the free fall along gravitational pull. This phenomena can also be explained sitting on the earth surface as their free fall suffers a centrifugal barrier due to the rotation. In this explanation, the term, centrifugal barrier, appears because earth is a non-inertial frame. Centrifugal force in a non intertial frame acts opposite to gravitational force.

The rotational energy / centrifugal barrier on a object depends on the radius of the circle linearly ; the circle is drawn around the axis of rotation from the point where the object placed. Now you can imagine that its radius get shorter and shorter towards the pole from the equator. Hence the barrier decreases if we move from equator to the both poles of earth. Hence garvitational force on a object i.e. its weight, so the g, becomes effectively maximum on the poles and minimum on the equator.

 

the slope of a line on a position vs time graph is the

a. velocity
b. time
c. distance
d. displacement

Answers

It's the velocity, but only the magnitude. It can't show the direction of the velocity. So it's better to call it speed.

An object weighs 980N on the earth’s surface (i) What is its mass? (ii) If the same object weighs 360N on another planet, find the force of gravity on that planet.

Answers

Weight = mass*gravity. Hence mass = 980/9.8 = 100kg. Gravity of planet 2 = weight/mass = 3.6 m/s^2

what is the meaning of energy

Answers

Answer:

[tex]\boxed{\mathrm{view \ explanation}}[/tex]

Explanation:

Energy is the capacity of an object to do work. Energy must be transferred to an object in order to do work. The SI unit of energy is Joules (J).

Answer:

See below

Explanation:

Energy is the "capacity/ability to do work". If the body has the ability to do work, we mean that the body possesses energy.

Units:

Energy is measured in Joules (J)

Types:

The two "main" types of energy are:

1) Kinetic Energy

2) Potential Energy

A Carnot air conditioner takes energy from the thermal energy of a room at 61°F and transfers it as heat to the outdoors, which is at 98°F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room?

Answers

Answer:

14.07 units of joules is removed for each joules of electricity used

Explanation:

The heated room temperature [tex]T_{c}[/tex] = 61 °F

The outside temperature [tex]T_{h}[/tex] = 98 °F

For conversion from fahrenheit to kelvin we use the equation

(32°F − 32) × 5/9 + 273.15

[tex]T_{c}[/tex] = 289.26

[tex]T_{h}[/tex] = 309.82

For air conditioning,

COP = [tex]\frac{T_{c} }{T_{h} -T_{c} }[/tex]

COP = [tex]\frac{289.26 }{309.82 -289.26 }[/tex]  = 14.07

This means that 14.07 units of joules is removed for each joules of electricity used

9. Which of the following is NOT a recommendation to help you succeed in this course?
Consistently and actively work in the course on a daily basis.
Wait until the end of the semester to complete all work.
Complete all assignments in a timely manner.
Contact your instructor if you have questions.

Answers

Answer:

Wait until the end of the semester to complete all work.

Explanation:

this is the obvious answer.

please mark me brainliest

Answer:

Wait until the end of the semester to complete all work

A 310 turn solenoid with a length of 18.0 cm and a radius of 1.60 cm carries a current of 1.90 A. A second coil of four turns is wrapped tightly around this solenoid, so it can be considered to have the same radius as the solenoid. The current in the 310 turn solenoid increases steadily to 5.00 A in 0.900 s.(a) Use Ampere's law to calculate the initial magnetic field in the middle of the 310 turn solenoid.T(b) Calculate the magnetic field of the 310 turn solenoid after 0.900 s.T(c) Calculate the area of the 4-turn coil.m2(d) Calculate the change in the magnetic flux through the 4-turn coil during the same period.Wb(e) Calculate the average induced emf in the 4-turn coil.VIs it equal to the instantaneous induced emf? Explain.(f) Why could contributions to the magnetic field by the current in the 4-turn coil be neglected in this calculation?

Answers

Answer:

Given that;

Number of turns in the solenoid N = 310

Length of the solenoid L = 18 cm = 0.18 m

Radius of the solenoid r = 1.60 cm = 0.016 m

Current in the first Circuit I₁ = 1.90A

Number of turns in second coil N₂ = 4

Final Current solenoid I₂ = 5.0 A

Time interval to change the time Δt = 0.9 s

a)

According to Ampere's law, magnetic field inside a conductor is calculated as;

B₁ = ц₀N₁I₁ / L

(ц₀ = 4π × 10⁻⁷  constant)

therefore we substitute

{(4π × 10⁻⁷) ×  310 × 1.9A} / 0.18m

= 0.0041 T

b)

Magnetic field inside the solenoid after t = 0.9

B₁ = ц₀N₁I₂ / L

= {(4π × 10⁻⁷) ×  310 × 5.0A} / 0.18m

= 0.0108 T

c)

Area of coil is

A = πr²

A = π ×  ( 0.016 )²

A = 0.000804 m²

d)

Change in magnetic influx is

dФ = (B₂ - B₁) A

= ( 0.0108 T - 0.0041 T) × 0.000804 m²

= 0.0000053868 ≈ 5.39 × 10⁻⁶

e)

Average induced emf is

e = -N₂ ( dФ / dt )

e = ( -4 ) ( 5.39 × 10⁻⁶ / 0.9)

e = - 2.39 × 10⁻⁵V ( NOTE, this is not equal to the instantaneous induced emf )

f)

The induced emf is very low, so the contributions to the magnetic field in the coil is Negative.

In 1869, Dmitri Mendeleev was trying to arrange the 65 known elements in a logical way. He arrived at the solution when he saw the elements arranged by atomic weight in a dream. He tried this arrangement and it worked! What is this an example of?

Answers

Answer:

Creative thinking

Explanation:

As you can see in the question above, when Mandleev needed to organize the chemical elements in a logical, organized and efficient way, he thought until he came to the conclusion of organizing them according to the atomic weight of each one. This is a clear example of creative thinking, which is the term that refers to the act of solving a problem based on thought and reasoning.

Answer:

Creative thinking

Explanation:

element x has two isotopes: x-27 and x-29. x-27 has an atomic mass of 26.975 and a relative abundance of 82.33%, and x-29 has an atomic mass of 29.018 and a relative abundance of 17.67%. calculate the atomic mass od element x. show your work

Answers

Answer:

27.336

Explanation:

The atomic mass is the weighted average of the atomic masses of the isotopes.  Simply multiply each isotopes's atomic mass by its relative abundance, then sum the results.

m = 0.8233 × 26.975 + 0.1767 × 29.018

m = 27.336


A particular electric car is supplied with 300 kJ of chemical energy by the battery. Of this, a total of 70.5 kJ of energy is wasted as heat.
Calculate the overall efficiency of the electric car.

Answers

Supplied energy=300kJ

Wasted energy=70.5J

Used energy:-

[tex]\\ \sf\longmapsto 300-70.5=229.5kJ[/tex]

We know

[tex]\boxed{\sf Efficiency=\dfrac{Used\:Energy}{Supplied\:Energy}\times 100}[/tex]

[tex]\\ \sf\longmapsto Efficiency=\dfrac{229.5}{300}\times 100[/tex]

[tex]\\ \sf\longmapsto Efficiency=\dfrac{229.5}{3}[/tex]

[tex]\\ \sf\longmapsto Efficiency=76.5\%[/tex]

The overall efficiency of the electric car = 76.5 %

To find the efficiency the given values are:

Energy supplied = 300 kJ

Energy wasted = 70.5 kJ

Define efficiency and calculate the value of efficiency.

      In the system the output energy is compared to the input energy is known as efficiency. That can be written as percentage ratio of output energy to the input energy.

Formula of efficiency is,

             Efficiency = ( E out / E in ) × 100

Here, Energy supplied = 300 kJ

so, energy used = Energy supplied - Energy wasted

                           = 300 - 70.5

                           =  229.5 kJ

Thus, substituting E out = 300 kJ , E in = 229.5 kJ

            Efficiency = ( 229.5 / 300 ) ×100

                             = 229.5 / 3

                             = 76.5

Hence, The overall efficiency of the electric car is 76.5 %

Learn more about efficiency,

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numeria
problems
lifted
Joy
1
لوووو
G. Solue the
following
A load
800 Nis
effort
If
the load is
laced at
a distance
Lo cun from
achat will be the
effort distance ?
Solher load ( l = 8oon
Effort
(e) = 200N
the fularum,​

Answers

Answer:

[tex] \boxed{40 \: cm}[/tex]

Explanation:

Load ( L ) = 800 N

Effort ( E ) = 200 N

Load distance ( LD ) = 10 cm

Effort distance ( ED ) = ?

now, Let's find the effort distance:

[tex] \mathsf{L \times LD = E \times ED}[/tex]

Plug the values

[tex] \mathsf{800 \times 10 = 200 \times ED}[/tex]

Multiply the numbers

[tex] \mathsf{8000 = 200 \: ED}[/tex]

Swipe the sides of the equation

[tex] \mathsf{200 \: ED = 8000}[/tex]

Divide both sides of the equation by 200

[tex] \mathsf{ \frac{200 \: ED }{200} = \frac{8000}{200} }[/tex]

Calculate

[tex] \mathsf{ED \: = \: 40 \: cm}[/tex]

Hope I helped!

Best regards!

numerical filing method is more scientific why give me 4 reason ​

Answers

Answer:

Numerical Methods are mathematical way to solve certain problems.Whether the equations are linear or nonlinear, efficient and robust numerical methods are required to solve the system of algebraic equations.

Analytical solutions are exact solutions based on mathematical principles.

However, the governing partial differential equations of fluid flow are complex and cannot be solved by analytical means. The partial differential equations are therefore converted into a system of algebraic equations that are subsequently solved through numerical methods to provide approximate solutions to the governing equations.

Although we rarely reach on exact answer , we can get really close to the exact answer much quicker than solve analytically.

Answer:

oh my god

Explanation:

how long answer is this

A 1000 kg car developed a snag and is standing in the middle of a road. The driver and a help pulled it with two ropes respectively with forces 200√2 N 45° east of south and 400N 30° north of east. Assuming negligible friction, find the acceleration of car

Answers

Answer:

Acceleration = 0.1464 m/s^2

Explanation:

From the question, the parameters given are:

Mass m = 1000 kg

The driver and a help pulled it with two ropes respectively with forces 200√2 N 45° east of south and 400N 30° north of east

Find the resultant force along the x axis.

(400 × cos30) - (200√2 × cos45)

346.4 - 200 = 146.4 N

therefore, the resultant force = 146.4N

The formula to use for the acceleration of the car is

F = ma

Where

F = resultant force

M = mass of the car

a = acceleration of the car

Substitute f and m into the formula

146.4 = 1000 × a

Make a the subject of formula

a = 146.4 / 1000

a = 0.1464 m/s^2

Therefore, the car accelerate at 0.1464 m/s^2

what is the kinetic energy of a 2,000-kg car moving at 20m/s

Answers

Answer:

400k

Explanation:

Formula for KE = [tex]\frac{1}{2} mv^{2}[/tex]

Plug in:

KE =  [tex]\frac{1}{2} mv^{2}[/tex]

KE =  [tex]\frac{1}{2}[/tex] × 2000 × 20^2

Solve:

1000 × 400 = 400,000 or 400k

Hope this helped.

Answer : 400000J OR 4×10^4J

Kinetic energy= 1/2mv^2

Here, m=2000kg; V=20m/s

1/2×2000×20×20=400,000J

Logam P dan Q sejenis. Logam P yang memiliki panjang 1 meter dipanaskan hingga mengalami kenaikan suhu 12ºC, akibatnya logam bertambah panjang 0,2 cm. Logam Q juga dipanaskan hingga mengalami kenaikan suhu 10°C dan panjangnya bertambah 0,1 cm. Tentukanlah panjang mula-mula logam Q!​

Answers

Answer:

I don't know ???

sorry

It takes Serina 1.81 hours to drive to school. Her route is 36 km long. What is Serina's average speed on her drive to school?

Answers

Answer:

60

Explanation:

because it shows he is moving at a low speed

Una onda se propaga en un medio P, de tal forma que recorre una distancia 8D en un tiempo 4T. La misma onda cuando se propaga por un medio Q recorre una distancia 4D en el mismo tiempo anterior, es decir, en 4T. Respecto a esta onda es correcto afirmar que *

Answers

Sabemos todo material tiene asociado un coeficiente de difracción n.

De tal forma que la velocidad de una onda electromagnetica que viaja a travez de dicho material, será:

v = c/n

donde c es la velocidad de la luz.

Con la información dada, podremos concluir que el coeficiente de difracción del medio Q es dos veces el del medio P.

Ahora veamos como llegamos a esto:

Sabemos que en el medio P, la onda recorre una distancia 8*D en un tiempo 4*T

entonces la velocidad de la onda en el medio P es:

[tex]V_p = \frac{8*D}{4*T} = 2*\frac{D}{T}[/tex]

Mientras que en el medio Q, recorre una distancia 4*D en un tiempo 4*T, por lo que la velocidad en el medio Q será:

[tex]V_Q = \frac{4*D}{4*T} = \frac{D}{T}[/tex]

Podemos ver que:

[tex]V_P = 2*V_Q[/tex]

Reescribiendo las velocidades como el cociente entre la velocidad de la luz y el correspondiente coeficiente de difracción obtenemos:

[tex]\frac{c}{n_P} = 2*\frac{c}{n_Q} \\\\n_Q = 2*n_P[/tex]

Es decir, podemos concluir que el coeficiente de difracción del medio Q es dos veces el del medio P.

Si quieres aprender más sobre el tema, puedes leer:

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A space rocket accelerates uniformly from rest to 160ms^-1 upwards in 4.0s, then travels with a constant speed of 160ms^-1 for the next 5.0s.
What is the initial acceleration of the rocket?

Answers

Answer:

40 ms¯².

Explanation:

To solve this problem, we shall illustrate the question with a diagram.

The attached photo gives a better understanding of the question.

From the attached photo:

Velocity (v) = 160 ms¯¹

Time (t) = 4 secs.

Acceleration (a) =?

Acceleration (a) = Velocity (v) /time (t)

a = v/t

a = 160/4

a = 40 ms¯²

Therefore, the initial acceleration of the rocket is 40 ms¯².

Comic-strip hero Superman meets an asteroid in outer space and hurls it at 800 m/s, as fast as a bullet. The asteroid is a thousand times more massive than Superman. In the strip, Superman is seen at rest after the throw. Taking physics into account, what would be his recoil speed (in km/s)?

Answers

Answer:

800km/s

Explanation:

Initial momentum = final momentum

the total momentum is zero, Before the release of the asteroid , but Superman and the asteroid are not moving.

So, according to the Conservation of momentum the total momentum when the astronaut is been thrown will equals to zero . Then we can say

Initial momentum = final momentum

Because the momentum of the Superman immediately the asteroid is been thrown is equal to the momentum of the asteroid

Momentum =(mass ×velocity)

the mass of the asteroid i= 1000M

Given velocity = 800 m/s,

momentum =(1000M)(800 m/s)

= 800,000M m/s.

to get the answer, we need to divide by Superman's mass, M, which gives his recoil velocity of 800,000 m/s.

But we're told to convert to km/ s

We know that 1m/s=0.001km/s

=(800,000M m/s)× (0.001km/s)

=800km/s

Therefore, his recoil speed (in km/s) is 800km/s

I need help asap please​

Answers

Answer:

I dont know answer Sorry For that thank u

How did Naya simulate the force exerted on the head?

Answers

Answer:

Naya used a machine that shoots tennis balls, like this one, to fire balls at a mannequin's head. ... Once Naya knew how much the mannequin moved with each hit, she could calculate how much force the head had received from each blow.

Answer:

She used a device to fire tennis balls at a mannequin head.

Explanation: EXACT ANSWER FROM PLATO/EDMENTUM!!! <3

if a girl is running along a straight road with uniform velocity 1.5 metre per second find the acceleration​

Answers

Answer:

Acceleration is 0.

Explanation:

Since the girl is running with a uniform velocity, meaning she is moving at a constant rate, she is not accelerating. Acceleration only occurs when the speed of an object increases, decreases, or if there is a change in direction.

This force governs atomic decay.

Answers

Answer:

The weak force governs the decay of a neutron into a proton (a process known as beta decay). The strong force binds quarks together into protons and neutrons (the residual strong force holds protons and neutrons together in the nucleus). Gravity governs the motion of an apple falling from a tree.

Explanation:

Answer:

Weak Nuclear force

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