A.
[tex]\begin{gathered} 1qt=946.353cm^3 \\ 5qt=\text{?} \\ \text{quantity}=946.353\times5 \\ \text{quantity}=4731.765cm^3 \end{gathered}[/tex]B.
[tex]\begin{gathered} 1\text{ gal=}3785.41\text{ }cm^3 \\ 2\text{ gal}=\text{?} \\ \text{quantity}=2\times3785.41 \\ \text{quantity}=7570.82cm^3 \end{gathered}[/tex]Tsunami waves generally carry a mass (m) of 770 kg of water, travel at a velocity (v) of approximately 10 m/s and have a height (h) of 10 m at landfall. The colony structures can withstand a total energy (TE) 135,000 J before catastrophic damage occurs.ANSWER (a) AND (b)(a) Using your answers from #4 and #5 calculate the total energy (TE) of a tsunami wave. TE = KE + PE (b) Using your calculations and the provided data, explain to the colonizing council whether this crash site can be used to start a colony.
ANSWER:
(a)
Potential energy = 75460 J
Kinetic energy = 38500 J
Total energy = 113960 J
(b)
The site can be used to start a colony.
STEP-BY-STEP EXPLANATION:
Given:
Mass (m) = 770 kg
Velocity (v) = 10m/s
Height (h) = 10 m
(a)
We calculate in each case the kinetic and potential energy by means of their formulas
[tex]\begin{gathered} E_k=\frac{1}{2}m\cdot v^2=\frac{1}{2}\cdot770\cdot10^2=38500\text{ J} \\ E_p=m\cdot g\cdot h=770\cdot9.8\cdot10=75460\text{ J} \end{gathered}[/tex]The total energy is the sum of both calculated energies:
[tex]\begin{gathered} E_T=38500+75460 \\ E_T=113960\text{ J} \end{gathered}[/tex](b)
Since the tsunami energy is less than the energy that can destroy the colony, then the site can support a permanent colony.
find an equation of the line with y intercept (0,7) and the slope of 1/2
Consider that a general way of writing a line equation is:
y = mx + b
where m is the slope of the line and b is the y coordinate of the y-intercept of the line.
Then, by using the given information:
m = 1/2
b = 7
You have the following equation of line:
y = 1/2*x + 7
According to Figure 2. the solar radiation Intensity 8.000 years ago was closest towhich of the following?490 watts/m20495 watts/m?O 500 watts/m2O 505 watts/m2
From the given figure, let's determine the solar radiation intensity 8000 years ago.
We can see the solar radiation intensity is represented on the left vertical (left side of the y-axis), while the number of years is represented on the x-axis.
Using the graph, at 8 thousand(8000) years ago, the radiation intensity was closest to 500 watts/m².
T
Please help with Question(ii). I don't understand the shown step of calculating the momentum of ball B. Especially after the third line 12+Pb=15.
Given:
m1 = mass 1 = 1kg
v1= initial velocity 1 = 12 m/s
m2= mass 2 = 3 kg
P after = momentum after collision = 15 kgm/s
(i)
Momentum of Ball A before collision
Momentum = mass x velocity
Pa = m1 v1
Replacing with the values given:
Pa = (1 kg) (12 m/s) = 12 kg m/s
(ii)
Momentum before = momentum after
Pa + Pb = P after
12 + Pb = 15
Since The ball B is travelling North, the distances travelled form a right triangle:
Apply pythagorean theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse= P after = 15
a & b are the other 2 legs of the triangle = Pa and Pb
Replacing:
15^2 = 12^2 + Pb^2
Solve for Pb
15^2 - 12^2 = pb^2
√15^2 -12^2 = Pb
pb= 9 kgms^2
A 65.0-kg basketball player jumps vertically and leaves the floor with a velocity of 1.80 m/s upward. (a) What impulse does the player experience? (b) What force does the floor exert on the player before the jump? (c) What is the total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump?
(a) The impulse experienced by the player is 117 Ns.
(b) The force the floor exert on the player before the jump is 637 N.
(c) The total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump is 260 N.
What impulse does the player experience?
The impulse experienced by the player is the change in the momentum of the player.
J = ΔP
J = m(v - u)
where;
m is the mass of the playerv is the final velocity of the player = 0u is the initial velocity of the player = - 1.8 m/s (negative because of upward direction)J = 65 x (0 + 1.8)
J = 117 Ns
The force the floor exert on the player before the jump is calculated as;
F = mg
where;
g is acceleration is due to gravityF = 65 x 9.8
F = 637 N
The total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump is calculated as;
F = ma
F = m(v/t)
F = (mv)/t
F = (65 x 1.8) / 0.45
F = 260 N
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Which of the following circuits can be used to measure the resistance of the heating element, shown as a resistor in the diagrams below?
In order to measure the resistance in the circuit, we need to know the voltage V and the current I in the circuit, this way we can calculate the resistance using the formula:
[tex]R=\frac{V}{I}[/tex]In order to calculate the current, we can use an amperemeter that must be in series with the circuit, this way it will not affect the circuit.
And in order to calculate the voltage, we can use a voltmeter that must be in parallel with the resistance, this way it will not affect the circuit.
The correct option that shows an amperemeter in series and a voltmeter in parallel is the fourth option.
10. ABC.Per=1200 NNet Force:Pit=600 NEngen-SONFrid=20 NPry=800 NPrax=800 NF50NWhich situation above would best describe free fall velocity?Which situation above would best describe a crane lifting an object?If situation C had a Fapp of 40N to the right, the net force on the object would beIf situation Chad Fapp of 20N to the right, the forces would be (balanced, unbalanced) and thehorizontal velocity would be (constant, + accelerating, - accelerating). Circle the correct terms
When the body is under free fall its apperaent weight will be zero.
Therefore
A worker is holding a filled gas cylinder still. Which two sentences are true about the energy of the filled gas cylinder?
A man in a blue dress holding a red color cylinder
It has no energy because it’s being held still.
It has gravitational potential energy because of its height.
Its atoms and molecules have thermal energy.
It has motion energy because it will fall if let go.
Its kinetic energy is being converted to potential energy.
The two sentences that are true about the energy of the filled gas cylinder are;
(b) It has gravitational potential energy because of its height
(d) It has motion energy because it will fall if let go.
What is the principle of conservation of conservation of energy?The principle or law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.
Based on this law, the kinetic energy of an object can be converted into potential energy and vice versa.
A filled gas cylinder held above the ground possesses gravitational potential energy and if the gas cylinder is held still, the kinetic energy is zero.
Thus, we can conclude that the following statements are true;
It has gravitational potential energy because of its height.It has motion energy because it will fall if let go.Learn more about conservation of energy here: https://brainly.com/question/166559
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The word _____ in contrast,refers to the accumulation of such a borrowing, year after year
Answer:
Budget
Explanation:
Have good day!!!
Using the work energy theorem, what is the final velocity of a roller coaster at the bottom of the hill. The coaster has a mass of 839 kg and starts at rest from the top of a hill that is 75 meters tall.
ANSWER
38.34 m/s
EXPLANATION
Given:
• The mass of the coaster, m = 839 kg
,• The initial height of the coaster, h = 75 m
,• The acceleration due to gravity, g = 9.8 m/s²
Find:
• The final velocity of the roller coaster at the bottom of the hill, v.
The roller coaster starts from rest, so at the top of the hill, it only has gravitational potential energy and no kinetic energy. Then, at the bottom of the hill, the roller coaster is in motion, to it has kinetic energy, and, because the difference of height with the reference - which is the bottom of the hill, is zero, it has no potential energy,
By the work-energy theorem, we have the equation,
[tex]KE_i+PE_i+W_{nc}=KE_f+PE_f_{}[/tex]As explained above, the initial kinetic energy is 0 and the final potential energy is also 0. If we assume that there is no friction, air resistance, or other external forces, then the work done by non-conservative forces is also 0,
[tex]PE_i=KE_f[/tex]Replace each kind of energy with the expression to obtain them,
[tex]m\cdot g\cdot h=\frac{1}{2}\cdot m\cdot v^2[/tex]The mass cancels out,
[tex]g\cdot h=\frac{1}{2}\cdot v^2[/tex]Solving for v,
[tex]v=\sqrt[]{2\cdot g\cdot h}[/tex]Replace with the known values and solve,
[tex]v=\sqrt[]{2\cdot9.8m/s^2\cdot75m}=\sqrt[]{1470m^2/s^2}\approx38.34m/s[/tex]Hence, the velocity of the roller coaster at the bottom of the hill is 38.34 m/s, rounded to the nearest hundredth.
Changes of state occur at segment _____________ and segment_______________.1st blankA-BB-CC-D2nd blank C-DD-EE-F
The change of phase takes place when the amount of heat added is changing the state and the temperature of the system remains constant.
In the given graph, the ice is changed into the water state through segment B-C.
Then the water is changed into a water vapor state in the segment D-E.
Hence, changes of state occur at segment B-C and segment D-E.
An air compressor has a volume of 100.L What volume of gas is pumped into the tank if the pressure goes from 750 torr to a pressure of 145 psi?Remember to convert pressure to atm. Refer to picture for conversions if needed.
ANSWER:
1000 L
STEP-BY-STEP EXPLANATION:
The first thing is to convert the unit of both pressures to atm, with the help of the conversion equivalences shown, just like this:
[tex]\begin{gathered} P_1=750\text{ torr }\cdot\frac{1\text{ atm}}{760\text{ torr}}=0.987\text{ atm} \\ P_2=145\text{ psi }\cdot\frac{1\text{ atm}}{14.7\text{ psi}}=9.87\text{ atm} \end{gathered}[/tex]Now, applying Boyle's Law, we calculate the value of the volume, like this:
[tex]\begin{gathered} P_1\cdot V_1=P_2\cdot V_2 \\ V_1=\frac{P_2\cdot V_2}{P_1} \\ \text{ replacing} \\ V_1=\frac{9.87\cdot100}{0.987}_{} \\ V_1=1000\text{ L} \end{gathered}[/tex]The volume of gas is 1000 L
Timothy wants to know how far his math class is from the orange tree across the street from the school. His feet are ideal feet (meaning they are 1 foot long. 1 foot is 12 inches). Timothy finds that the orange tree is 159 feet from the door of the math classroom. He wants to know that distance in kilometers (km).a. Convert from feet to inches (1 ft =12 in)b. Convert from inches to centimeters (1 in =2.54c. Conver from centimeters to meters (1m = 100cm)d. Convert from meters to kilometers (1km=1000m)
a) 1 foot = 12 inches
159 feet = 159 x 12 = 1908
The distance in inches is 1908 inches
b) 1 inch = 2.54 cm
1908 inches = 1908 x 2.54 = 4846.32
The distance in centimeters is 4846.32 cm
c) 100 cm = 1 m
4846.32 cm = 4846.32/100 = 48.4632
The distance in meters is 48.4632 m
d) 1000m = 1 km
48.4632 m = 48.4632/1000 = 0.0484632
The distance in kilometers is 0.0484632 km
To make peanut butter, a machine grinds peanuts into a paste. Which of the following can be considered as a process of this system?Question 16 options:PeanutsMachine grinds peanutsPeanut butter
A process is an action that involves individual items, not the items themselves.
Answer: Machine grinds peanuts
A truck covers 40.0 m in 9.00 s while uniformly slowing down to a final velocity of 2.20 m/s.(a) Find the truck's original speed. m/s(b) Find its acceleration. m/s2
Given:
The distance covered by truck: d = 40.0 m
The time taken to cover the distance is: t = 9.00 s
The final velocity of the truck is: v2 = 2.20 m/s
To find:
a) the speed of the truck.
b) the acceleration
Explanation:
a)
The speed of the truck before it slows down can be calculated as:
[tex]d=\frac{1}{2}(v_2+v_1)t[/tex]Substituting the values in the above equation, we get
[tex]\begin{gathered} 40=\frac{1}{2}(2.20+v_1)\times9 \\ \\ \frac{40\times2}{9}-2.20=v_1 \\ \\ v_1=6.69\text{ m/s} \end{gathered}[/tex]b)
The truck is initially moving at a speed of 6.69 m/s. It then slows down to the final velocity of 2.20 m/s. The acceleration of the truck can be determined as:
[tex]d=v_1t+\frac{1}{2}at^2[/tex]Substituting the values in the above equation, we get:
[tex]\begin{gathered} 40=6.69\times9+\frac{1}{2}\times a\times9^2 \\ \\ 40=60.21+40.5a \\ \\ a=\frac{40-60.21}{40.5} \\ \\ a=-0.499 \\ \\ a\approx-0.5\text{ m/s}^2 \end{gathered}[/tex]Final answer:
a) The original speed of the truck is 6.69 m/s.
b) The acceleration of the truck is - 0.5 m/s^2.
The acceleration of gravity depends on (click all that apply)
The expression for the acceleration due to gravity can be given as,
[tex]g=\frac{GM}{R^2}[/tex]Here, g is the acceleration due to gravity, G is the gravitational constant, M is the mass of planet and R is the distance from the center of planet.
Therefore, the acceleration due to gravity depends upon the distance from center of planet and the mass of planet.
The critical angle for a certain liquid-air surface is 20°. What is the index of refraction of this liquid?
ANSWER
[tex]\begin{equation*} 2.92 \end{equation*}[/tex]EXPLANATION
To find the index of refraction of the liquid, we have to apply the formula for critical angle:
[tex]\theta=\sin^{-1}(\frac{n_r}{n_i})[/tex]where nr = refractive index of air = 1
ni = refractive index of liquid
Hence, by substituting the given values into the equation, we have that the index of refraction of the liquid is:
[tex]\begin{gathered} 20=\sin^{-1}(\frac{1}{n_i}) \\ \sin20=\frac{1}{n_i} \\ n_i=\frac{1}{\sin20} \\ n_i=2.92 \end{gathered}[/tex]That is the answer.
Bryan slid a glass of O] for Dalton across a counter with a speed of 2.1m/s. Unfortunately, Dalton missed it! If the countertop was 1.1m above the floor a) how long did it take for the glass to hit the floor? b) how far horizontally did the glass travel in the air?
A. The time taken for the glass to hit the floor is 0.5 s
B. The horizontal distance travelled by the glass in the air is 1.1 m
A. How to determine the time
The following data were obtained from the question:
Height (h) = 1.1 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) = ?The time taken to hit the ground can be obtained as follow:
h = ½gt²
1.1 = ½ × 9.8 × t²
1.1 = 4.9 × t²
Divide both side by 4.9
t² = 1.1 / 4.9
Take the square root of both side
t = √(1.1 / 4.9)
t = 0.5 s
Thus, the time taken is 0.5 s
B. How to determine horizontal distance
The horizontal distance can be obatined as follow:
Horizontal speed (u) = 2.1 m/sTime (t) = 0.5 sHorizont distance (s) = ?s = ut
s = 2.1 × 0.5
s = 1.1 m
Thus, the horizontal distance is 1.1 m
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list advantages and disadvantages of surface tension
please i really need this urgently
Advantages of Surface tension are -
It gathers water into a ball.
It permits a distinct boundary layer that is similar to a non-Newtonian liquid.
It enables water to rise into a paintbrush through capillary action.
It permits rain to fall as drops as opposed to a stifling mass.
It enables smooth surfaces to form as concrete and liquid metals solidify.
Disadvantages of Surface tension are -
The behavior of water would alter if surface tension were eliminated, some of these changes being related to surface tension's drawbacks. Washing clothing is one example that is close to home. Detergent is required while washing garments due to the comparatively high surface tension of water. Reduced surface tension enables laundry water to fully permeate the garments for better cleaning as part of the task of laundry detergent. It would take far less detergent to wash clothes if water had a naturally low surface tension.
When you want to create a fine water spray, such as with a lawn sprinkler, surface tension again becomes an issue. Surface tension makes it harder to divide water into tiny droplets. Sprinklers could operate on a hose with less pressure if they were used with water that had a lower surface tension.
What is a surface tension ?
Surface tension is the propensity for liquid surfaces that are at rest to condense into the smallest surface area. Razor blades and insects (like water striders), which have a higher density than water, can float on the surface of the water without even becoming partially buried because to surface tension.
Surface tension at liquid-air contacts originates from the liquid molecules' stronger attraction to one another due to cohesion than to the air molecules (due to adhesion).
There are primarily two mechanisms at work. One causes the liquid to constrict by exerting an inward push on the surface molecules. The second force is tangential and parallel to the liquid's surface. The surface tension is the common name for this tangential force.
Overall, the liquid acts as though an elastic membrane was stretched over its surface. However, this comparison should not be drawn too far because surface tension is a characteristic of liquid-air or liquid-vapor interfaces, but the tension in an elastic membrane depends on how much it is deformed.
Advantages of Surface tension are -
It gathers water into a ball.
It permits a distinct boundary layer that is similar to a non-Newtonian liquid.
It enables water to rise into a paintbrush through capillary action.
It permits rain to fall as drops as opposed to a stifling mass.
It enables smooth surfaces to form as concrete and liquid metals solidify.
Disadvantages of Surface tension are -
The behavior of water would alter if surface tension were eliminated, some of these changes being related to surface tension's drawbacks. Washing clothing is one example that is close to home. Detergent is required while washing garments due to the comparatively high surface tension of water. Reduced surface tension enables laundry water to fully permeate the garments for better cleaning as part of the task of laundry detergent. It would take far less detergent to wash clothes if water had a naturally low surface tension.
When you want to create a fine water spray, such as with a lawn sprinkler, surface tension again becomes an issue. Surface tension makes it harder to divide water into tiny droplets. Sprinklers could operate on a hose with less pressure if they were used with water that had a lower surface tension.
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A student on skateboard pushes off from the top of small hill with a apees of 2.0m/s, and then geos down the hill with a constant acceleration of 0.5 m/s2
After traveling a distancie 12.0m, how fast is the student going?
The final velocity of the student after travelling 12 m is 4 m/s.
What is the final velocity of the student?
The final velocity of the student is determined by applying the following Kinematic equation.
v² = u² + 2as
where;
u is the initial velocity of the studentv is the final velocity of the studenta is the acceleration of the students is the distance travelled by the studentv² = (2)² + 2(0.5)(12)
v² = 16
v = √16
v = 4 m/s
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If a 4 kg ball is dropped from rest and falls without air resistance, what is its speed after 0.5 seconds?
Answer:
4.9 m/s
Explanation:
The velocity of the ball after 5 seconds can be calculated using the following equation
[tex]v_f=v_i+at[/tex]vi = the initial velocity, in this case, it is equal to 0 because the ball is dropped from the rest
a = acceleration, this is the acceleration due to gravity so it is -9.8 m/s²
t = time, it is equal to 0.5 s
So, replacing the values, we get:
[tex]\begin{gathered} v_f=0-9.8(0.5) \\ v_f=-4.9\text{ m/s} \end{gathered}[/tex]Therefore, the speed after 0.5 seconds is 4.9 m/s
A quantity of steam (650 g) at 116°C is condensed, and the resulting water is frozen into ice at 0°C. How much heat was removed?answer in:____ kcal
Total heat removed = 473.04 kCal
Explanation:Heat removed to convert the 116°C to 100°C steam
[tex]\begin{gathered} H=mc(\theta_2-\theta_1) \\ \\ H=650(1.996)(116-100) \\ \\ H=20758.4J \end{gathered}[/tex]Heat removed from 100°C of steam to 100°C of water (Latent heat of condensation)
[tex]\begin{gathered} H_c=650\times2257 \\ \\ H_c=1467050J \end{gathered}[/tex]Heat removed from 100°C water to 0°C water
[tex]\begin{gathered} H_w=650\times4.2\times100 \\ \\ H_w=273000J \end{gathered}[/tex]Heat removed from 0°C water to 0°C ice
[tex]\begin{gathered} H_i=mL_f \\ \\ H_i=650(336) \\ \\ H_i=218400J \end{gathered}[/tex]Total heat removed = 20758.4J + 1467050 + 273000 + 218400
Total heat removed = 1979208.4 J
Convert to kilocalorie
Total heat removed = 1979208.4/4184
Total heat removed = 473.04 kCal
How many cubic inches are there in 3.25 yd3?Express the volume in cubic inches to three significant figures.What is the mass in grams of 16.86 mL of acetone?Express your answer to four significant figures and include the appropriate units.What is the volume in milliliters of 7.06 g of acetone?Express your answer to three significant figures and include the appropriate units.
Answer:
[tex]\text{ 3.25 yd}^3=151,632in^3[/tex]Explanation: We need to convert cubic-yards into cubic inches, this can be simply done as follows:
[tex]\frac{46656\text{ Cubic inches}}{1\text{ Cubic Yard}}^{}[/tex]Therefore we have:
[tex]\begin{gathered} 3.25\text{ Cubic yards }\times\text{ }\frac{46656\text{ Cubic Inches}}{1\text{ Cubic Yard}}=151,632\text{ Cubic Inches} \\ \therefore\rightarrow \\ \text{ 3.25 yd}^3=151,632in^3 \end{gathered}[/tex]Mass/energy equivalence is expressed mathematically in which of the following expressions?
Check each option to see how it relates to different concepts.
Option 1: E=hf
This equation tells the energy carried by an electromagnetic wave with frequency f.
Option 2: E=mc
This equation is not correct, since the left member is measured in units of energy and the right member does not.
Option 3: E=(1/2)mv^2
This equation relates the energy of a moving object with its mass and its velocity. It is known as kinetic energy.
Option 4: E=mc^2
Since c is a constant (the speed of light), this equation relates the energy of an object with its mass.
Therefore, the mass/energy equivalence is expressed mathematically in the equation:
[tex]E=mc^2[/tex]critical mass depends on ___. Check all that apply.A. the polarityB. the purityC. the densityD. the shape
Related to the amount of a fissionable material's critical mass depends on different factors.
These factors are:
- the shape of the material
- the density
- the purity
all last factors are related to the critical mass, becasue of all of them change the efficiency at which neutrons continue the fission procedure.
What is the image distance if a 5.00 cm tall object is placed 2.33 cm from a converging lens with a focal length of 5.75 cm?0.603cm1.66cm-0.255cm-3.92cm
We will have the following:
First, we will recall that:
[tex]\frac{1}{f}=\frac{1}{v}+\frac{1}{u}[/tex]That is:
[tex]\begin{gathered} \frac{1}{5.75}=\frac{1}{2.33}+\frac{1}{u}\Rightarrow\frac{1}{u}=-\frac{1368}{5359} \\ \\ \Rightarrow u=-\frac{5359}{1368}\Rightarrow u\approx-3.92 \end{gathered}[/tex]So, the image distance is approximately -3.92 cm.
According to Newton’s second law of motion,how much force will be required to accelerate an object at the same rate if it mass is reduced by half ?
According to Newton's second law of motion,
[tex]\text{Force = mass}\times acceleration[/tex]Let the initial force be F, acceleration be a and the initial mass be m.
The acceleration is the same but now the mass is reduced by half.
So, the force will be
[tex]\begin{gathered} F^{\prime}=\frac{m}{2}\times a \\ =\frac{F}{2} \end{gathered}[/tex]Thus, the force will also be half of the initial force if the mass is reduced by half.
if i put my spoon in the microwave what will happen
If you put your spoon in the microwave, nothing will happen to it as long as it has round edges and it is not touching any sides of the microwave.
Putting a spoon in the microwaveSpoons are generally made from stainless steel. Stainless steels are iron and chromium. In some cases, other metals such as nickel are thrown into the mix.
Thus, being made of metals, these stainless steels are good conductors of heat and electricity.
A microwave works by heating foods put into it using electromagnetic radiation in the microwave frequency range. Electromagnetic radiation causes the molecules of food to rotate and produce thermal energy.
If the spoon touches the side of the microwave, sparks may result. Otherwise, it is totally fine because spoons usually have round edges. With rough edges, the waves may be reflected back and forth and create sparks.
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The position of a particle is F(t) = 4.01²î - 3.0ĵ +2.03 km. (a) What is the velocity of the particle at 0 s and at 1.0 s? (b) What is the average velocity between 0 s and 1.0
The velocity of the particle at 0 s and at 1.0 and the average velocity between 0 s and 1.0
a)[tex]\vec{V}(0)=0 m / s[/tex]
[tex]\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s[/tex]
b)[tex](4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}[/tex]
This is further explained below.
What is the average velocity?Generally, the equation for the Position is mathematically given as
F(t) = 4.01²î - 3.0ĵ +2.03 km.
Therefore
[tex]\begin{aligned}&\vec{r}(t)=\left(4 t^2 \hat{l}-3 \hat{\jmath}+2 t^3 \hat{k}\right) m \\&\vec{V}(t)=\frac{d \vec{r}(t)}{d t}=\left(8 t \hat{\imath}+6 t^2 \hat{k}\right) m / s\end{aligned}[/tex]
For A
[tex]\begin{aligned}&\vec{V}(0)=0 m / s \\&\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s\end{aligned}[/tex]
For B
[tex]\text { Average velocity } &=\frac{\text { Total displacement }}{\text { time interval }} \\[/tex]
[tex]=\frac{\vec{r}(1)-\vec{r}(0)}{1} \\&=4 \hat{\imath}-3 \hat{\jmath}+2 \hat{k}-\left(-3 \hat{\jmath}^{\prime}\right) \\&=(4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}\end{aligned}[/tex]
In conclusion, The speed of the particle at 0 seconds and at 1.0 seconds, as well as the average speed between 0 seconds and 1.0 seconds
a)[tex]\vec{V}(0)=0 m / s[/tex]
[tex]\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s[/tex]
b)[tex](4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}[/tex]
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Peter is trying to ignite the hotplate by turning the gas knob. Suppose thatthe minimum moment of couple about the center of the gas knob requiredto ignite the hotplate is 0.3 N m. Calculate the minimum force (F, and F2)that required to exert. Given that the diameter of gas knob is 5 cm.
the minimum force is 6 Newtons
Explanation
A moment of a force, or a torque, is a measure of a force's tendency to cause a body to rotate. The moment depends on both the force, and on the position at which the force acts, it is given by the expression
[tex]M=F\cdot d\text{ }[/tex]where F is the exerted force and d is the distance
Step 1
then, let
[tex]\begin{gathered} M=\text{0}.3\text{ Nm} \\ F=F \\ \text{distance}=\text{ 5 cm= }\frac{5}{100}m=0.05\text{ m} \\ \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} M=F\cdot d\text{ } \\ 0.3\text{ Nm=F}\cdot0.05\text{ m} \\ \text{divide both sides by 0.05 m} \\ \frac{0.3\text{ Nm}}{0.05\text{ m}}\text{=}\frac{\text{F}\cdot0.05\text{ m}}{0.05\text{ m}} \\ 6N=F \end{gathered}[/tex]therefore, the minimum force is 6 Newtons
I hope this helps you