v^2 = k am sn,
where k is a dimensionless constant.
we have to tell the whether it is dimensional or dimensionless
v = m/sec dimesions
a = m/sec^2 dimesion, m = m
v^2 = m^2 / sec^2 = k m/sec^2 * m
k = dimesionless constant.
Dimension is a measurable extent, such as the three principal dimensions of an object of width, height, and depthdimension is of many types radial, angular, linear etc.Reference Dimensions is a Dimension without a tolerance, used for information purposes only. A reference is a repeat of a given dimension or established from other values one dimension is practically not found.To know more about Dimension visit : https://brainly.com/question/1374629
#SPJ4
3. A large crane lifts a 25,000 kg mass in the air. The amount of work that must be done by the
crane's lifting components is 2.2 X 10'J (Wo). If the efficiency of the crane is 22%, how much
useful work is done on the mass (Wou)?
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the concept of Efficiency.
Here we can see that, the Input work is given as 2.2 x 10^7 J and the efficiency is given as 22%
The efficiency is => 22% => 22/100.
so we get as,
E = W(output) /W(input)
hence, W(output) = E x W(input)
so we get as,
W(output) = (22/100) x 2.2 x 10^7
=> W(output) = 0.22 x 2.2 x 10^7 => 0.484 x 10^7
hence, W(output) = 4.84 x 10^6 J
The useful work done on the mass is 4.84 x 10^6 J
With friction turned on, let the skater do one back-and-forth on the half pipe. Use
the grid. Does he reach the same height as when he started?
The skater does indeed reach the same height on either side of the track With friction turned on.
The only thing that will change is how long it takes for the skater to come to a rest during the scenario. Only the skater's initial height when placed onto the track affects the overall energy, which remains constant.Potential energy is transformed into kinetic energy as the skateboarder descends the ramp. Some of the system's energy is changed into heat energy by friction. The energy cannot be returned to the system's potential or kinetic energy once the kinetic energy has been transformed into heat.For more information on friction kindly visit to
https://brainly.com/question/13000653
#SPJ1
In which of these reactions is energy released?
A. Exothermic reactions
B. No reactions
C. All reactions
D. Endothermic reactions
Answer:
exothermic reaction
Explanation:
Exothermic reactions are reactions or processes that release energy, usually in the form of heat or light. In an exothermic reaction, energy is released because the total energy of the products is less than the total energy of the reactants.
I want to use the 250m drop. The loss in the pipeline is 10 m. The total power of the aberration is 15,000 kW, and the specific speed is 32
A smaller Pelton aberration is used, the rotation speed is 600 rpm, the bucket speed and the jet speed ratio are 0.42, and the
The efficiency is 85%, and the velocity coefficient of the nozzle is 0.97. Find the following values.
(a) the number of aberrations required (b) the diameter of the rotary wheel (c) the diameter of the jet
To solve the given problem, we can use the Pelton turbine equation and various efficiency formulas.
To calculate the discharge (Q), we need to convert the power (P) from kilowatts (kW) to watts (W) using the conversion factor: 1 kW = 1000 W.
P = ρQgHη
Q ≈ 78.05 m^3/s
Now, we can substitute the values of N, H, and Q into the specific speed formula:
32 = 600√(240) / (78.05^0.75)
we can rearrange the equation:
Z = (600 * 15.49193338) / (32 * (78.05^0.75))
Z ≈ 15
(b) To calculate the diameter of the runner/wheel (D), we can use the formula:
D = (0.262 * √(Q)) / N
Substituting the given values:
D = (0.262 * √(78.05)) / 600
D ≈ 0.014 m
(c) The diameter of the jet (d) can be calculated using the formula for the velocity coefficient (Cv):
Cv = Q / (A * V)
To learn more about Pelton turbine equation follow:
https://brainly.com/question/33219023
#SPJ11
What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45.0° when it passes through a diffraction grating that has 500.0 lines per mm?
236 nm
353 nm
943 nm
1414 nm
Answer:
D) 1414 nm
Explanation:
This is correct on Edge.
Using the equation dsin(angle)=n(wavelength), we can solve for wavelength.
First we must convert the 500 lines per mm to nm. We do this by 1/500, giving you 0.002. Then move the decimal over six places to the right, resulting in 2000.
Then by plugging in the other values, we have 2000sin(45)=1(wavelength).
N is one because we are just solving for a first-order band.
So 2000sin(45)=wavelength
By using a calculator, we can see that the wavelength equals approximately 1414nm.
I hope this helped. If it did, I would really appreciate a Brainliest!!
Have a great day:)
Answer:
1414
Explanation:
took the test :)
What is the focal length of a lens
Answer:
The focal length of a lens is the distance between the lens and the image sensor when the subject is in focus, usually stated in millimeters.
this is refering to a camera lens, not glasses and what not, glasses do not have a focus length, only equipment that has the ability to focus
Explanation:
May I have brainliest please? :)
how elements are arranged in the groups of periodic table
Which of the following skills that you learn while participating in a team sport is also a life skill that employers look for?
A.
Showing respect to others
B. Working well with others
c.
Problem solving
D
All of the above
Answer:
The answer is all of the above
Explanation:
Answer:
D
Explanation:
A 5kg box rests on a table. a 3 kg box rests on top of the 5 kg box. what is the normal force from the table?
a. 19.6 n
b. 29.4 n
c. 49 n
d. 78.4 n
==> The total mass resting on the table is (5 kg + 3 kg) = 8 kg.
==> The total weight of that mass is (8 kg) x (9.8 m/s) = 78.4 newtons
==> The boxes are stacked. So the table doesn't know if the weight on it is coming from one box, 2 boxes, 3 boxes, or 100 boxes in a stack. The table only knows that there is a downward force of 78.4 newtons on it.
==> The table stands in a Physics classroom, and it soaks up everything it hears there. It knows that every action produces an equal and opposite reaction, and that forces always occur in pairs.
Ever since the day it was only a pile of lumber out behind the hardware store in the rain, the table has known that in order to maintain the good reputation of tables all over the world, it must resist the weight of anything placed upon it with an identical upward force. This is the normal thing for all good tables to do, up to the ultimate structural limit of their materials and construction, and it is known as the "normal force".
So the table in your question provides a normal force of 78.4 newtons. (d)
234 oz to tons using the table method (US)
Answer:
234 oz = 0.0066339 t.
Explanation:
Boom Logic...
Formula:
F = ma
m = F/a
a = F/m
1. What is the force of the object, if it has a mass of 25kg moving 3 m/s2?
Answer:
55N
Explanation:
Using Newton's second law of motion:
F=ma
Force=mass × acceleration
F=25×2.2
F=55N
So 55 Newtons are needed
A 3.00 kg crate is pulled along a frictionless surface with a force of 55.0 N at 25.00 to the
horizontal so that it accelerates directly to the right. What is the crate's acceleration?
A gasoline engine has a power output of 190 kW (about 255 hp). Its thermal efficiency is33.0%.
(a) How much heat must be supplied to the engine persecond?
J
(b) How much heat is discarded by the engine per second?
J
The formula for thermal efficiency:
Thermal efficiency = (Useful work output) / (Heat input)
Given that the power output of the engine is 190 kW and the thermal efficiency is 33.0%, we can proceed with the calculations.
First, we need to calculate the useful work output of the engine. Since power is the rate at which work is done, we can convert the power output from kilowatts to joules per second (Watts).
Power output = 190 kW = 190,000 W
The useful work output can be calculated using the equation:
Useful work output = Power output * Time
Since we are interested in the heat supplied per second, the time can be taken as 1 second.
Useful work output = 190,000 W * 1 s = 190,000 J
Next, we can use the formula for thermal efficiency to find the heat input:
Thermal efficiency = (Useful work output) / (Heat input)
Rearranging the equation, we can solve for the heat input:
Heat input = (Useful work output) / (Thermal efficiency)
Heat input = 190,000 J / 0.33
Heat input ≈ 575,757 J
Therefore, the heat that must be supplied to the engine per second is approximately 575,757 J.
(b) How much heat is discarded by the engine per second?
Since the thermal efficiency is given as the ratio of useful work output to heat input, the heat discarded by the engine can be calculated as the difference between the heat input and the useful work output.
Heat discarded = Heat input - Useful work output
Heat discarded = 575,757 J - 190,000 J
Heat discarded ≈ 385,757 J
Therefore, the heat discarded by the engine per second is approximately 385,757 J.
To know more about thermal efficiency:
https://brainly.com/question/12950772
#SPJ1
A non -viscous incompressible fluid is pumped steadily into the narrow end of a long tapered pipe and emerges from the wide end . The pressure at the input is greater than at the output . A possible explanation is :
Answer:
v₂ =\(( \frac{r_1}{r_2})^2 \ v_1\)
Explanation:
This phenomenon is explained by the continuity equation in fluids
v₁A₁ = v₂A₂
where the subscript 1 is for the input narrow part and the subscript 2 for the wide part
v₂ = \(\frac{A_1}{A_2} v_1\)
consider the cross section at each point
A₁ = π r₁²
A₂ = π r₂²
we substitute
v₂ =\(( \frac{r_1}{r_2})^2 \ v_1\)
therefore the exit velocity is less than the entrance velocity of the fluid.
We can also analyze the situation using Bernoulli's equation
P₁ + ρ g v₁² + ρ g y₁ = P₂ + ρ g v₂² + ρ g y²
if we assume a horizontal system y₁ = y₂
P₁-P₂ = ρ g (v₂² - v₁²)
A farsighted man uses eyeglasses with a refractive power of 3.80 diopters. Wearing the glasses 0.0250 m from his eyes, he is able to read books held no closer than 0.280 m from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?
The correct contact lens prescription for the farsighted man would be -34.8 diopters.
The man's current eyeglasses have a refractive power of 3.80 diopters and are held 0.0250 m from his eyes. He is able to read books held no closer than 0.280 m from his eyes with them on.
To find the correct contact lens prescription, we need to use the formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
We know that do = 0.280 m and di = -0.0250 m (since the contact lens will be directly on the eye), so we can solve for f.
Plugging in the values, we get f = -0.0287 m.
To find the power of the contact lens, we use the formula P = 1/f, which gives us P = -34.8 diopters.
Learn more about refractive power at
https://brainly.com/question/31744248
#SPJ11
experiment to show how mechanical, heat, chemical, solar, and/or electrical energy may be converted from one or more types of energy to another
The chemical energy in food is converted by the body into mechanical energy and heat. The chemical energy in coal is converted into electrical energy at a power plant. The chemical energy in a battery can also supply electrical power by means of electrolysis.
How can energy be converted from one form to another?
Energy can change from one form to another. For example, when you switch on a light bulb, electrical energy changes to thermal energy and light energy. A car changes energy stored in the chemical bonds of gasoline to several different forms. A chemical reaction in the engine changes chemical energy to light
How is chemical energy converted to mechanical energy and heat energy in the body?
In the human body chemical energy in the form of the glucose in our food is turned into mechanical energy in the process of movements such as running or lifting heavy objects. The muscles serve as a transducer, through muscle contraction energy is transformed from chemical to mechanical energy.
Learn more about energy conversion :
brainly.com/question/15105485
#SPJ4
Why would there be different considerations for regular lenses vs sunglasses and what would be the preference?
a plumbing contractor needs to deliver 200 lengths of steel pipe to a construction site. each cylindrical steel pipe is 160 cm long, has an outer diameter of 6 cm, and has an inner diameter of 5 cm. the contractor needs to know whether her quarter-ton truck can handle the weight of the pipes. hint: steel has a density of about 7.7 g cm3 . one ton equals 1000 kg. a. what is the mass of these 200 pipes in kilograms?
The mass of the 200 steel pipes is approximately 3484.46 kg.
Mass of the steel pipes in kilograms, we need to first calculate their volume and then multiply it by the density of steel.
Each steel pipe has a length of 160 cm and an outer diameter of 6 cm, which means that its radius is 3 cm. The inner diameter is 5 cm, which means that the thickness of the pipe wall is (6 cm - 5 cm) / 2 = 0.5 cm.
Using these dimensions, we can calculate the volume of each pipe as follows:
Volume of each pipe = π * (r_outer - r_inner) * length
= π * (3 cm) * 160 cm - π * (2.5 cm) * 160 cm
= 2261.9464 cm
So the total volume of 200 pipes is:
Total volume = 200 * 2261.9464 cm = 452389.28 cm
Now we can calculate the mass of the pipes by multiplying the volume by the density of steel:
Mass = Total volume * Density of steel
= 452389.28 cm * 7.7 g/cm^3
= 3,484,461.456 g
Finally, we can convert the mass from grams to kilograms by dividing by 1000:
Mass in kilograms = 3,484,461.456 g / 1000
= 3484.461456 kg
Therefore, the mass of the 200 steel pipes is approximately 3484.46 kg.
Learn more about mass Visit: brainly.com/question/86444
#SPJ4
How are fission and fusion similar?
A. A small fraction of the reactant mass is converted into small amounts of energy.
B. A large fraction of the reactant mass is converted into small amounts of energy.
C. A large fraction of the reactant mass is converted into large amounts of energy.
D. A small fraction of the reactant mass is converted to large amounts of energy.
Answer:
C
Explanation:
Fusion and fission are similar in that they both release large amounts of energy. Nuclear fusion is a process in which two nuclei join to form a larger nucleus. Nuclear fission is a process in which a nucleus splits into two smaller nuclei.
How are scientists able to predict when and where the next eclipse will occur?
Answer:
When the Earth and sun are perfectly lined up, then it will happen. They can tell when it's going to happen.
Explanation:
This is why it only happens in some places. Some days it's not sunny out, so it's not going to happen.
an image formed on a screen is always
Answer:
diminished and erect( upright)
Explanation:
What is the relationship between resistance and current.
Answer:
They are inversely proportional with each other. \(R\) ∝ \(\frac{1}{I}\)
Explanation:
By the equation V=IR, assume V is constant.
Since I and R are on the same side,
if I increase, R decreases, or the vice versa.
how do the principle of motion apply to the design and construction of machine and vehicle?
A power station that is being started up for the first time generates 6120 MWh of energy over a 10 hour period. (i) If the rated power at full capacity is 660 MW, calculate how long it takes the power station to reach its full power output. (You may assume a constant increase in power from zero to full power) (ii) State what type of power station can be started up fastest and explain why the start-up times for other types of power station are slower. Explain briefly, how this is relevant to optimising the usage of windfarms. c) What is the Bremsstrahlung effect and how can it be avoided in shielding design? d) Sketch the electromagnetic field output from an antenna, describing in detail the two main regions in the output field.
(i)Therefore, it takes approximately 9.27 hours to reach its full power output.(ii)It is necessary to have quick-start power sources, this helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.(c)The Bremsstrahlung effect needs to be considered to ensure proper radiation protection.(d) The near-field region is characterized by strong electric and magnetic fields while the far-field region represents the radiation zone.
(i) To calculate the time it takes for the power station to reach its full power output, we can use the formula:
Energy = Power × Time
Given that the power station generates 6120 MWh of energy over a 10-hour period and the rated power at full capacity is 660 MW, we can rearrange the formula to solve for time:
Time = Energy ÷ Power
Converting the energy to watt-hours (Wh):
Energy = 6120 MWh × 1,000,000 Wh/MWh = 6,120,000,000 Wh
Converting the power to watt-hours (Wh):
Power = 660 MW × 1,000,000 Wh/MW = 660,000,000 Wh
Now we can calculate the time:
Time = 6,120,000,000 Wh ÷ 660,000,000 Wh ≈ 9.27 hours
Therefore, it takes approximately 9.27 hours (or 9 hours and 16 minutes) for the power station to reach its full power output.
(ii) The type of power station that can be started up fastest is a gas-fired power station. Gas-fired power stations can reach full power output relatively quickly because they use natural gas combustion to produce energy.
In contrast, other types of power stations, such as coal-fired or nuclear power stations, have longer start-up times. Coal-fired power stations require time to heat up the boiler and generate steam, while nuclear power stations need to go through a complex series of procedures to ensure safe and controlled nuclear reactions.
This is relevant to optimizing the usage of windfarms because wind power is intermittent and dependent on the availability of wind. This helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.
(c) The Bremsstrahlung effect is a phenomenon that occurs when charged particles, such as electrons, are decelerated or deflected by the electric fields of atomic nuclei or other charged particles. As a result, they emit electromagnetic radiation in the form of X-rays or gamma rays.
In shielding design, the Bremsstrahlung effect needs to be considered to ensure proper radiation protection. These materials effectively absorb and attenuate the emitted X-rays and gamma rays, reducing the exposure of individuals to harmful radiation.
(d) The electromagnetic field output from an antenna can be represented by two main regions:
Near-field region: This region is closest to the antenna and is also known as the reactive near-field. It extends from the antenna's surface up to a distance typically equal to one wavelength. In the near-field region, the electromagnetic field is characterized by strong electric and magnetic field components.
Far-field region: Also known as the radiating or the Fraunhofer region, this region extends beyond the near-field region.The electric and magnetic fields are perpendicular to each other and to the direction of propagation. The far-field region is further divided into the "Fresnel region," which is closer to the antenna and has some characteristics of the near field, and the "Fraunhofer region," which is farther away and exhibits the properties of the far-field.
The transition between the near-field and the far-field regions is gradual and depends on the antenna's size and operating frequency. The size of the antenna and the distance from it determine the boundary between these regions.
In summary, the near-field region is characterized by strong electric and magnetic fields, while the far-field region represents the radiation zone where the energy is radiated away as electromagnetic waves.
To know more about power station:
https://brainly.com/question/32772374
#SPJ4
Through brain imaging, we have observed that men process emotion _____
Through brain imaging, we have observed that men process emotions differently.
Brain imaging studies have revealed that there are some differences in how men and women process emotions. While it is important to note that these differences are not absolute and there is significant individual variation, research suggests that certain brain regions involved in emotional processing may show variations between genders. For example, studies have found that men may rely more on the amygdala, a brain structure associated with the processing of emotional stimuli, while women may exhibit greater involvement of the prefrontal cortex, which is involved in emotional regulation and decision-making.
It's essential to approach these findings with caution, as emotions are complex and influenced by various factors including social and cultural contexts. The observed differences in brain processing of emotions between men and women should be seen as part of a broader understanding of emotional experiences rather than definitive conclusions.
To know more about prefrontal cortex, visit
https://brainly.com/question/30746925
#SPJ11
A sled is pulled at a constant velocity across a horizontal snow surface. If a force of 100 N is being applied to the sled rope parallel to the ground, what is the force of friction between the sled and the snow?
Answer:
60.18 N
Explanation:
Given that:
The force applied on the sled = 100 N
Suppose, the angle between the sled rope and the ground = 53°
The horizontal force which acts in the horizontal direction can be expressed as:
\(F_x = F \ cos \theta\)
\(F_x = 100 \ cos (53)\)
\(F_x = 60.18 \ N\)
But if the angle between the sled rope is parallel to the ground. Then, we use an angle on a straight line which is = 180°
\(F_x = F \ cos \theta\)
\(F_x = 100 \ cos (180)\)
= 100 × -1
= -100 N
We now define a quantity_______, called the total mechanical energy of our system
We now define a quantity the sum of the potential energy and the kinetic energy is called the total mechanical energy of our system.
What is Total Mechanical energy?
The energy a body has as a result of movement or position is known as mechanical energy. The energy that is released by falling from a particular position is a good example. As the literal driving force of the world around us, whether it be natural or man-made, mechanical energy is one of the fundamentals studied in mechanical engineering. In joules, mechanical energy is measured.
The sum of a body's potential energy and kinetic energy is referred to as total mechanical energy. The total of the two forms of mechanical energy in a single occurrence is constant. The ball's kinetic and potential energies change quickly as it rises and falls, but their combined total remains constant.E = K + U.
The ball starts to lose kinetic energy as it rises. The conversion of energy to potential energy, or heat, which is essentially a chaotic mixture of kinetic and potential energy, is the only way energy can actually be lost. The ball develops momentum as it falls back down, increasing its kinetic energy.This kinetic energy does not just appear. Instead, the ball's potential energy—which it accumulated while rising—is now being converted into kinetic energy.To know more about Total Mechanical energy ,refer to:
https://brainly.com/question/15277710
#SPJ1
Which two factors are used to calculate kinetic energy?
A The chemical formula for the object
B. The velocity of an object
c. The mass of an object
D. The height of an object
E . The density of an object
Answer:
B. The velocity of an object
c. The mass of an object
Explanation:
If the acceleration of a school bus over a given time interval is zero, how does the instantaneous velocity of that school bus at any instant during that interval compare to its average velocity over the interval?.
Both the average and instantaneous velocities well be same over the given interval if the acceleration is zero.
What is instantaneous velocity?Instantaneous velocity is the rate of differential change of displacement with respect differential change in time. Mathematically -
v = dx/dt
Given is the acceleration of a school bus over a given time interval as zero.
For acceleration over a given time interval to be zero, it must be ensured that the the velocity of the object should remain constant. Mathematically-
a = (v - u)/(t₂ - t₁)
For acceleration [a] = 0, v = u. Therefore -
a = 0
The instantaneous velocity for zero acceleration between the time interval t₁ to t₂ will be equal to initial velocity only -
dx/dt = u
This will be the instantaneous velocity and is equal to (u) at any instant.
Now -
dx = u dt
Integrating both sides, we get -
∫dx = ∫u dt
x = ut
Therefore, the average velocity will be =
v(avg) = x/Δt = ut/Δt
Now -
t = Δt for any specific time interval. Therefore -
v(avg) = ut/t = u
This is the average velocity and it is equal to (u).
Therefore, both the average and instantaneous velocities well be same over the given interval if the acceleration is zero.
To solve more questions on instantaneous velocity, visit the link below-
https://brainly.com/question/17475447
#SPJ1
At time t=​0, a particle is located at the point ​(1​,1​,3​). It travels in a straight line to the point ​(5​,9​,4​), has speed 6 at ​(1​,1​,3​) and constant acceleration 4i+8j+k. Find an equation for the position vector r​(t) of the particle at time t.
Ignoring the malformed character, it looks like you're saying you have particle initially located at (1, 1, 3) that travels in a straight line to (5, 9, 4) with initial speed 6 and constant acceleration vector 4i + 8j + k.
Use the fundamental theorem of calculus to determine the velocity function for the particle:
\(\vec v(t) = \vec v(0) + \displaystyle \int_0^t \vec a(u) \, du\)
The particle moves in the same direction as the vector
(5i + 9j + 4k) - (i + j + 3k) = 4i + 8j + k
which has magnitude
√(4² + 8² + 1²) = √81 = 9
Normalize the direction vector by dividing it by its magnitude:
(4i + 8j + k)/9 = 4/9 i + 8/9 j + 1/9 k
The particle has initial speed 6, so we must scale this unit vector by a factor of 1/6 to get the initial velocity vector:
6 (4/9 i + 8/9 j + 1/9 k) = 8/3 i + 16/3 j + 2/3 k
Solve for v(t) :
\(\vec v(t) = \dfrac83\vec\imath + \dfrac{16}3\vec\jmath + \dfrac23\vec k + \displaystyle \int_0^t \left(4\vec\imath + 8\vec\jmath+\vec k\right) \, du\)
\(\vec v(t) = \dfrac83\vec\imath + \dfrac{16}3\vec\jmath + \dfrac23\vec k + \left(4t\,\vec\imath + 8t\,\vec\jmath+t\,\vec k\right)\)
\(\vec v(t) = \left(\dfrac83+4t\right)\vec\imath + \left(\dfrac{16}3+8t\right)\vec\jmath + \left(\dfrac23+t\right)\vec k\)
Use the fundamental theorem again to find the position vector r(t) :
\(\vec r(t) = \vec r(0) + \displaystyle \int_0^t \vec v(u) \, du\)
\(\vec r(t) = \vec\imath+\vec\jmath+3\vec k + \displaystyle \int_0^t \left(\left(\dfrac83+4u\right)\vec\imath + \left(\dfrac{16}3+8u\right)\vec\jmath + \left(\dfrac23+u\right)\vec k\right) \, du\)
\(\vec r(t) = \vec\imath+\vec\jmath+3\vec k + \left(\left(\dfrac83 t+2t^2\right)\vec\imath + \left(\dfrac{16}3t+4t^2\right)\vec\jmath + \left(\dfrac23t+\dfrac12t^2\right)\vec k\right)\)
\(\vec r(t) = \left(1+\dfrac83 t+2t^2\right)\vec\imath + \left(1+\dfrac{16}3t+4t^2\right)\vec\jmath + \left(3+\dfrac23t+\dfrac12t^2\right)\vec k\)