an ink-jet printer steers charged ink drops vertically. each drop of ink has a mass of 10-11 kg, and a charge due to 751896 extra electrons. it goes through two electrodes that gives a vertical acceleration of 104 m/s2. the deflecting electric field is mv/m.

The​ particle's velocity at as a product of its speed and direction is equal to 10 . [tex](\frac{8}{10},0,\frac{6}{10} )[/tex]

Velocity is the directional speed of a moving item as an indication of its rate of change in position as seen from a specific frame of reference and measured by a specific time standard (e.g., 60 km/h northbound). The idea of velocity is crucial in kinematics, the part of classical mechanics that explains the motion of bodies.

A physical vector quantity called velocity requires both magnitude and direction to be defined. Speed is a coherent derived unit that expresses the scalar absolute value (magnitude) of velocity. Its quantity is expressed in SI units (metric system) of metres per second (m/s or ms1). For example, "5 meters per second" is a scalar while "5 meters per second east" is a vector.

The particle's velocity is the derivative of its position. The particle's acceleration is the derivative of its velocity. You can calculate the velocity and acceleration as follows:

[tex]\vec{v}(t)=\frac{d r}{d t}=\frac{d}{d t}(8 t+5) \vec{i}+\frac{d}{d t}\left(8 t^2-2\right) \vec{j}+\frac{d}{d t}(6 t) \vec{k}=8 \vec{\imath}+16 t \vec{j}+6 \vec{k}[/tex]

[tex]\vec{a}(t)=\frac{d v}{d t}=\frac{d}{d t}(8) \vec{i}+\frac{d}{d t}(16 t) \vec{j}+\frac{d}{d t}(6) \vec{k}=0 \vec{i}+16 \vec{j}+0 k[/tex]

The velocity at t = 0 is  [tex]\vec{v}(0)=8 \vec{i}+0 \vec{j}+6 k[/tex]

if the speed at t = 0 is [tex]||\vec{v}(0)||[/tex] = 10 then the velocity at t = 0 can be written as a product of the speed at t = 0 & the direction at t = 0 is

[tex]\vec{v}(0)=\|\vec{v}(0)\| \frac{\vec{v}(0)}{\|\vec{v}(0)\|}=10 \cdot\left(\frac{8}{10}, 0, \frac{6}{10}\right)[/tex]

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Full question

The equation r (t) = (8t + 5)i + (8t^2 - 2)j + (6t )k is the position of a particle in space at time t. Find the​ particle's velocity and acceleration vectors. Then write the​ particle's velocity at t equals 0 as a product of its speed and direction. What is the velocity​ vector?

Newton's second law of motion states that "the acceleration of an object is equal to the force on an object divided by the mass of the object.​"

Newton's second law of motion is also called the law of acceleration as it tells us about the acceleration of a moving object under the influence of an unbalanced force or net force not equal to zero.

According to the law, the acceleration of an object is directly proportional to the force on the object and inversely proportional to the mass of the object.

Acceleration a ∝ Force F                                                                       ....1

Acceleration a ∝ 1/Mass m                                                                    ....2

From 1 and 2  Acceleration a = [tex]\frac{Force}{Mass}[/tex]

Therefore, Newton's second law of motion states that "the acceleration of an object is equal to the force on an object divided by the mass of the object.​"

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They found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

Vector addition is the operation of adding two or more vectors together into a vector sum. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

When the two students added a vector for a moving object’s position at t=2s to a motion diagram. They found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

Thus, they found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

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Answer: 1325t miles

Explanation: you have to divide all of them

The average speed of the tennis ball is 3 m/s.

Average speed can be defined as the ratio of the total distance to the total time covered by the body. The S.I unit of average speed is m/s.

To calculate the formula below.

Formula:

Where:

From  the question,

Given:

Substitute these values into equation 1

Hence, The average speed of the tennis ball is 3 m/s.

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The model that best represents this phenomenon is called Osmosis

In osmosis, a semi-permeable membrane allows the solvent to pass from a higher solvent concentration to a lower solvent concentration (or, to put it another way, from a lower solute concentration to a higher solute concentration).

As a result, the dialysis bag with the highest concentrated starch solution will absorb the most water from the outside (present in the beaker).

Line A thus displays the information gathered from the bag containing the highest concentrated starch solution.

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The answer is:Area=1/2×b×h

Answer:

A= b×h ÷ 2

Explanation:

The Area of a triangle formula is the Base multiplied by the Height, then divided by 2

Juggler will catch the second ball 1 second after catching the first ball as the first ball comes down 1 second earlier than the second.

Two balls are thrown into the air. The first ball goes up with a velocity of 9.8m/s and the second ball goes with a velocity of 14.7m/s. We have to find out the Time difference between the balls when both of them land in the hand. We have Newton's first equation :  v = u + at =>  t = (v-u)/a

where, v = Final velocity, u = Initial velocity, a=g = Acceleration of gravity, and t = Time

For First ball, v1 = 9.8m/s, u1 = 0, g = 9.8 (acceleration for gravity),             t1 = time and multiplying the equation by 2 for marking journey of balls for both going up and down

              => t1 = 2(v1-u1)/g    =>  t1 = (9.8-0)/9.8

              => t1 = 2 seconds

For second ball, v2 = 14.7m/s, u2 = 0, g = 9.8 (acceleration for gravity),

t2 = time & multiplying the equation by 2 for marking journey of ball for both going up and down  => t2 = 2(v2-u2)/g  

              => t2 = (14.7-0)/9.8  => t2 = 3 seconds

Difference between the time taken by both balls t = t2-t1

                    => t = 1 second

So the second ball lands after 1 second.

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The gravitational energy of the brick before it was dropped was 507.15 J.

Let us assume that the brick is dropped from the rest at a height of h meters above the ground and reaches the ground at a speed of 26.0 m/s.

Given in question

Initial Velocity = u = 0 m/s ( dropped from rest )

Final Velocity = v = 26.0 m/s

Acceleration = a = g = 9.8 m/s

Using the third equation of motion,

v² - u² = 2ah

Put in the values, we get

(26)² - (0)² = 2×9.8×h

19.6h = 676

h = 676/19.6

h = 34.5 meters

So the brick was at the height of 34.5 meters before it was dropped. The gravitational potential energy of the body is given by

U = mgh, where

m = mass = 1.5 kg

g = acceleration due to gravity = 9.8 m/s²

h = height above the ground = 34.5 m

Put in the values, we get

U = 1.5×9.8×34.5 J

U = 507.15 J

Therefore, the gravitational energy of the brick before it was dropped was 507.15 J.

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The direction of the resultant of the three forces can be seen as resultant is 78.25 lb and its direction can be calculated as [tex]\theta[/tex] =65.19°.

To find component in x-direction,

Fx = p3 cos(30) + p2 cos (30+45) - p1 cos (40)

Fx = 46 cos(30) + 45 cos (75) - 20 cos (40)

Fx = 46x 0.866 + 45x 0.2588 - 20x 0.766

Fx = 39.836+11.646-15.32

Fx = 36.165 lb

To find component in y direction,

Fy = -p3 sin(30) - p2 sin (30+45) - p1 sin(40)

= -[ 46x 0.5 + 45x 0.96 + 20x0.16]

= -[23 + 43.2 + 3.2]

= - 69.4 lb

Fr = [tex]\sqrt{fy^{2} +fx^{2} }[/tex]

=[tex]\sqrt{(-69.4)^{2} + (36.165)^{2} }[/tex]

=[tex]\sqrt{4816.36+1307.9}[/tex]

=[tex]\sqrt{6124.26}[/tex]

= 78.25 lb

Then to find [tex]\theta[/tex]

[tex]\theta\\[/tex] = [tex]tan^{-1} \frac{fy}{fx}[/tex]

=[tex]tan^{-1}[/tex] (78.25/36.165)

= [tex]tan^{-1}[/tex] (2.163)

= 65.19°

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The graph shown in the first option shows a reasonable representation of the velocities of the lion and the gazelle as functions of time, therefore the correct answer is option A.

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.

As given in the problem if a lion is running at constant speed toward a gazelle that is standing still, as shown in the top figure above.

Thus, the correct answer is option A.

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Answer:

250 m/s      (VERY fast !)

Explanation:

30 km = 30 000 m

30 000 m / 120 s = 250 m/s

Using dimensional analysis; L²/T⁴ = 2 * L²/T⁴

Thus, v² = u² + 2as is dimensionally correct.

Dimensional analysis is the process whereby the various quantities of measurement are expressed in their basic unit or the fundamental units from which they are derived.

The fundamental units which are used in dimensional analysis is done is:

To check if v² = u² + 2as is dimensionally correct:

unit of v = m/s = L/T

unit of u = L/T

unit of a = L/T²

s = L

(L/T)² = (L/T)² + L * L/T²

L²/T⁴ = L²/T⁴ + L²/T⁴

L²/T⁴ = 2 * L²/T⁴

The expression, v² = u² + 2as is dimensionally correct.

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The boat had sailed 1130km.

Initial Boat travel time = 7 hours.

The boat's initial speed is 80 km/h

The boat's current speed is 95 km/h.

Boat travel time at present = 6 hours.

Total nautical miles traveled =?

Solution:

Speed = distance / time.

The distance = Speed * Time

1. Distance = 80 km/h x 7 hours

  Distance = 560 km

2. Distance = 95km/h x 6hours

   Distance = 570 km

Hence, total distance = 560km + 570km

                                    = 1130km

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Ohm's Law is a formula used to determine how voltage, current, and resistance in an electrical circuit relate to one another.

Use Ohm's Law to calculate the following:

a) The voltage required to produce a current of 2A in a 12ohms resistor.

To scientists, Einstein's Relativity equation (E = mc2) is as fundamental as Ohm's Law (E = IR).

E = I x R

The difference in electric potential between two points, which is defined as the work required per unit of charge to move a test charge between the two points, is known as voltage, electric potential difference, electric pressure, or electric tension.

The formula reads voltage = current x resistance, or V = A x, or volts = amps x ohms.

Therefore, Voltage required = 2 * 12 = 24 volts

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The tension force would be 7.62N. Its angle of equilibrium would be 70.23°

For equilibrium,

for direction X,

Tcos([tex]\theta[/tex]-36.87°) = 8cos (36.87°) → 1

For direction Y,

9 = 8sin36.87° + Tsin([tex]\theta\\[/tex]-36.87°)

Tsin([tex]\theta\\[/tex]-36.87°) = 9- 8sin(36.87°) → 2

Now dividing equation 2 by 1,

tan([tex]\theta\\[/tex]-36.87°) = [tex]\frac{9-8*3/5}{8*4/5}[/tex]

tan([tex]\theta\\[/tex]-36.87°) = 0.66

[tex]\theta\\[/tex] - 36.87°= [tex]tan^{-1}[/tex](0.66)

[tex]\theta\\[/tex] - 36.87° = 33.42°

⇒ [tex]\theta[/tex] = 40.29°

Now from equation 1,

Tcos(33.42°) = 8cos(36.87°)

T = [tex]\frac{8*4/5}{0.84}[/tex]

T = 7.62N

Thus, we get the tension force as 7.62N

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Answer:

See below

Explanation:

With N   at 0 degrees    

   35 degrees south of west becomes  90 + 35 = 125 °

x component      50 km  cos 125  = - 28.7 km

y component       50 km sin 125 =   41 km

the maximum size of fuse permitted in a single phase is 18.75 ampere.

POWER = amount of energy transferred per unit time.

Power = voltage x current

power = 4500 volt-ampere

voltage = 240 volt

current = power/voltage

       = 4500/240

      = 18.74 ampere

the maximum size of fuse permitted in a single phase is 18.75 ampere.

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Rate of acceleration for a 5 kg grocery cart that’s being pushed with 50 N is 10 m/sec^2. The value of acceleration can be calculated with the help of following formula Fnet = m . a

Fnet is the  net force acting on the shopping cart

m is the mass of the grocery cart

a is the acceleration of the shopping cart

So on using the formula we get

Fnet = m . a

So on putting the values we get

Fnet = 50 N

m = 5kg

a = ?

50 = 5.a

On calculating we get the value of acceleration

a = 10 m/sec^2

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Water depth Bathyscaphes can submerge at a depth of h=5 km=5000 m.

the seawater's particular weight,

γ=10.1kN/m3

Through the equation, the density of the seawater and its specific weight are connected.

γ=ρg→(I)

where rho is the seawater's density and g is the acceleration brought on by gravity.

Given is the pressure at a depth of h meters. ,

P=ρgh→(II)

When equation I is substituted, equation (ii),

P=γh

About substituting

P=10.1×103×5000=50.5×106Pa=50.5MPa

1 Pascal =1.45×10−4psI

50.5 MPa corresponds to

50.5MPa=50.5×106×1.45×10−4psI=7322.5psI

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Larger diameter, capabilities of the better gathering of light, and better resolving power are those advantages that a large diameter astronomical telescope has over a telescope of a smaller diameter.

The larger the lens or mirror which is having the diameter or aperture, the telescope will then gather more light and will be at higher resolution as the viewer has the chance to see fine in detail it can. Larger scopes also have focal lengths of longer size, which means the magnifications will be greater and the sizes of images are possible with accessibility by both the eye as well as the camera.

A larger telescope mirror is a type that allows us to view the fainter objects farther into the region of space, therefore the larger one in round nature is better. The shape does not matter just as long as it can bring light to the focus point.

Large telescopes will be having several merits over their smaller counterparts, and the concerned resolution will be as how much in detail we are able to see a celestial object is the first priority. Generally, the resolution depends mainly on two things the stability of the atmosphere as well as the aperture present in your telescope. The user can only control any one of these factors.

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When the wavelength of light is decreased the ejected electrons would have greater kinetic energy.

A kind of energy that an item or particle possesses as a result of its mobility is known as kinetic energy.

When an item undergoes work—the transfer of energy—by being subjected to a net force, it accelerates and consequently obtains kinetic energy.

An object's kinetic energy is the energy it has as a result of motion.

Kinetic energy is the force that drives an object's motion.

Kinetic energy can be found in moving objects such as a bullet traveling at high speed or a person walking.

The energy brought on by the random, continuous bouncing of atoms or molecules is another illustration of kinetic energy.

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J. J. Thomson used a cathode-ray tube to calculate the charge-to-mass ratio of the electron. The deflection of cathode rays towards the positively charged surface and emission of green light at the far end of the tube confirmed that they are negatively charged particles.

In 1897, J.J Thomson performed a cathode ray tube experiment to determine the charge-to-mass ratio of electrons.

Due to high voltage, a beam of particles was allowed to flow from the negatively charged end to the positively charged end of the tube.

One end of the tube was painted with phosphorous. When electrons struck the wall a green spark was observed which confirmed the presence of negatively charged particles i.e. electrons.

To put it simply, cathode rays came from the cathode tube and deflected towards a positively charged plate showing that they are negatively charged particles.

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If the measurement is taken for four different times for same weight and is always different then the balance is precise but not accurate.

There are numerous instruments available for measuring mass in various settings. The use of gravitational interaction between objects is one of them, along with balances and scales, measurement transducers, vibrating tube sensors, Newtonian mass measurement devices, and balances and scales.

The kilogram, which is defined as equal to 6.6260 x 10³⁴joule second in terms of Planck's constant, is the unit of mass in the International System of Units (SI). A joule is equal to one kilogram multiplied by one square meter per second.

A beam balance is always used to determine mass. Because a spring balance measures weight rather than mass, it will read differently depending on where you are on the planet.

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The speed as the stone hits the ground is 29.4 m/s

The distance at which the stone fell is 44.1 m.

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

An example of an amphetamine is speed. It is a central nervous system stimulant that releases significant amounts of dopamine. Dopamine is a neurotransmitter in the brain linked to reward and pleasure.

Although it is occasionally used to refer to other amphetamines, speed is the street name for amphetamine sulphate. It typically appears as an off-white or pinkish powder and occasionally as crystals. It can also be found in the form of a paste, which is often white, grey, or brown in color and can be grippy and wet.

Speed can be defined as the ratio of distance to time.

(a) To calculate the speed at which the stone hit the ground, we use the formula below.

Formula:

v = u+gt............ Equation 1

Where:

v = Final speed of the stone

u = Initial speed of the stone = 0 m/s

t = time = 3 seconds

g = acceleration due to gravity = 9.8 m/s²

Substitute the values above into equation 1

v = 0+3×9.8

v = 29.4 m/s

(b) To calculate the distance the stone fell, we use the formula below.

S = ut+gt²/2........... Equation 2

Where:

S = Distance

Solving for S by substituting into equation 2

S = (0×3)+(9.8×3²)/2

S = 44.1 m

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The deceleration of the car from a velocity of 100ms-1 to a final velocity of 20ms-1 in 10 seconds is 8ms-2.

We are aware that acceleration refers to an object's rate of increase in speed, and deceleration refers to an object's rate of decrease in speed.

Because it must be reported as a magnitude and a direction, acceleration is a vector. Negative and positive signs are used to denote the direction in circumstances of one-dimensional motion. Negative indicators indicate that the object is slowing down.

The unit of measurement is the meter per second square, or ms-2.

We know that

v= u + at,

where,

v= final velocity

u= initial velocity

t= time

a= acceleration

According to the question,

u= 100ms-1

v= 20ms-1

t= 10s

a=?

so, v = u + at

substituting the values in the equation, we get:

20 = 100 + 10a

a= -8 ms-2

Here, the negative sign shows that the car is decelerating,

Thus, deceleration is 8ms-2.

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The direction of the car will not change and the speed of the car at time of 2 seconds will be 4 m/s.

The size of the change in an object's position over time or the size of the change in that object's position per unit of time makes the speed of an object, also known as v in kinematics, a scalar number. The instantaneous speed is the upper limit of the average speed as the duration of the time interval gets closer to zero. 

According to the question,

Initial Speed, u is 12 m/s,

Time, t at 2 seconds and,

acceleration is -4 m/s².

Now by using Equation of motion :

v=u+at

v=12+(- 4 m/s²)(2 sec)

V=12-8

V= 4 m/s.

Hence, the speed of the car will be 4 m/s at time 2 seconds and the direction of the car will not change.

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Answer:

9.8 m/s2

Explanation:

the Acceleration is due and represented by g and the answer to that is 9.8 m/s2

The force between two masses when the distance between those two masses is increased by a factor of four is 0.5 N

We know that,

F = G [tex]m_{1}[/tex] [tex]m_{2}[/tex] / [tex]r^{2}[/tex]

where,

F = Force

G = Constant

[tex]m_{1}[/tex], [tex]m_{2}[/tex] = Masses

r = Distance between those two forces

Given that,

F = 8 N

When the distance between those two masses is increased by a factor of four,

[tex]F^{'}[/tex] = G [tex]m_{1}[/tex] [tex]m_{2}[/tex] / [tex]( 4r)^{2}[/tex]

[tex]F^{'}[/tex] = F / 16

[tex]F^{'}[/tex] = 8 / 16 = 1 / 2

[tex]F^{'}[/tex] = 0.5 N

Force is a phenomenon which can cause an objects motion to change. It causes an object with mass to change its velocity.

Therefore, the force between two masses when the distance between those two masses is increased by a factor of four is 0.5 N

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