If you start at point A and walk 5 m east to point B and then 5 m south to point C, what is your displacement?
5.0 m, east
5.0 m, south
7.07 m, southeast
50. m, northwest
Answers
The resultant displacement of the object as we can see is 7.07 m south east as the object is moving to the south east.
What is the displacement?We know that displacement has to do with the change in the position of an object with time in a specific direction. I want to clarify here that the difference between the distance and the displacement is the fact that the displacement must have a particular direction.
We know that since the displacement is a vector that we have to be able to apply the principles of the vector to be able to find the resultant displacement.
Then we have;
Resultant displacement =√ 5^2 + 5^2
= 7.07 m south east
The displacement of the object is it is moving is obtained as 7.07 m south east in that given direction.
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Related Questions
the nucleus of a uranium atom has a diameter of 1.5×10−14m and a mass of 4.0×10−25kg. part a what is the density of the nucleus? express your answer with the approp
Answers
The nucleus of a uranium atom has a diameter of 1.5×10−14m and a mass of 4.0×10−25kg, thus the density of the uranium nucleus is 2.24×10^17 kg/m^3.
To calculate the density of the uranium nucleus, we need to use the formula: density = mass/volume. As we know the mass of the nucleus is 4.0×10−25kg, we need to find the volume of the nucleus. The volume of a sphere is calculated using the formula V = (4/3)πr^3. Given that the diameter of the nucleus is 1.5×10−14m, the radius can be calculated as 0.75×10−14m.
Plugging this value into the formula, we get the volume of the nucleus as 1.77×10−43m^3. Now, we can calculate the density by dividing the mass by volume. This gives us the density of the uranium nucleus as 2.24×10^17 kg/m^3. This means that the nucleus is incredibly dense and heavy, given its tiny size.
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When a charged capacitor is disconnected from a battery and the area of the plates is decreasing; describe what is happening to the electric field in the capacitor and explain why.
Answers
When a charged capacitor is disconnected from a battery and the area of the plates is decreasing, the electric field in the capacitor is increasing.
This can be explained by considering the relationship between the electric field, the charge on the plates, and the area of the plates.The electric field in a capacitor is given by the formula E = Q / (ε₀A), where E represents the electric field, Q is the charge on the plates, ε₀ is the permittivity of free space, and A is the area of the plates. When the capacitor is disconnected from the battery, the charge on the plates remains constant. However, as the area of the plates decreases, the denominator in the formula for the electric field (ε₀A) decreases. Since the charge remains the same, this reduction in the denominator results in an increase in the electric field E.
In simpler terms, the electric field in a capacitor is inversely proportional to the area of the plates. As the area decreases, the electric field strengthens. This occurs because the same amount of charge is now concentrated on a smaller surface area, leading to a higher electric field intensity between the plates. Therefore, when a charged capacitor is disconnected from a battery and the area of the plates is decreasing, the electric field in the capacitor increases due to the concentration of charge on a smaller surface area.
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Cell phones use electromagnetic radiation with energy of about 1.08J/mol photons. Calculate the wavelength and frequency that can be used to describe light with this energy.
Answers
We know that the energy of electromagnetic radiation is given by:
\(E=hf\)where E is the energy, h is Planck's constant and f is the frequency. Before we can use this formula we need to convert the amount of energy given to J so let's do that:
\(1.08\text{ }\frac{J}{mol}\cdot\frac{1\text{ mol}}{6.022\times10^{23}}=1.793\times10^{-24}J\)Now that we have the energy of the radiation, we plug it on the energy equation and solve for the frequency:
\(\begin{gathered} 1.793\times10^{-24}=6.63^\times10^{-34}f \\ f=\frac{1.793\times10^{-24}}{6.63\times10^{-34}} \\ f=2.704\times10^9 \end{gathered}\)Therefore, the frequency of the cell phone electromagnetic radiation is:
\(2.704\times10^9\text{ Hz}\)Now that we know the frequency we just need to remember that the frequency and wavelength of electromagnetic radiation are related by:
\(\lambda=\frac{c}{f}\)Then we have:
\(\begin{gathered} \lambda=\frac{3\times10^8}{2.704\times10^9} \\ \lambda=0.111 \end{gathered}\)Therefore, the wavelength is 0.111 m
Explain your answers to 9a and 9b in terms of Newton's laws of motion.
Answers
Answer:i One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
Explanation:
Why are the 5 senses important to us
Answers
Answer:
Sight, taste, hearing, touch, and smell are all important because they help us with our daily and social lives.
Explanation:
hope this helps
have a good day
Answer:
They help us interact with the world around us. (and to sense stuff of course!)
Explanation:
find the measure of each interior angle and each exterior angle of a regular 45-gon.
Answers
Each Interior angle of a regular 45-gon is 172° and each exterior angle is 188°.
A polygon is defined as the closed 2-D shape with straight sides. For example a pentagon is the closed of 5 straight sides. Interior angle is defined as the angle subtended by two straight sides inside the traverse. Whereas exterior angle defined as the angle subtended by two straight sides outside the closed traverse. A 45-gon is closed traverse with 45 straight sides.
The sum of all the interior angles of a polygon is (2n-4)×90.
The sum of all the exterior angles of a polygon is (2n+4)×90
Where n number of straight sides.
So the sum of all interior angles of 45-gon is (2×45-4)×90 = 7740
Each interior angle is 7740/45 = 172°
So the sum of all exterior angles of 45-gon is (2×45+4)×90 = 8460
Each exterior angle is 8460/45 = 188°
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A measure of the pull of gravity on an object.
Group of answer choices
Mass
Height
Weight
Gravitational Potential Energy
Answers
Answer:
weight.................
Can someone pls help me
Answers
A ball is thrown straight upward at 10 m/s. Ideally (no air resistance), the ball will return to the thrower's hand with a speed of
a) 5 m/s
b) 10 m/s
c) 0 m/s
d) 20 m/s
Answers
This is the answer it just asked me to put more 20 characters but the answer is B
Ideally in no air resistance, the ball will return to the thrower's hand with a speed of 10 m/s. Thus, the correct option is B.
What is the Speed of ball?Speed is the distance covered by an object with respect to time taken. It can also be defined as the change in the position of an object with respect to time. It is a scalar quantity as it has only magnitude and no direction.
The ball which is thrown straight upward in the sky with a speed of 10 m/s will return back to the thrower's hands with a speed of 10m/s in the ideal case of no air resistance because during this situation, no acceleration takes place. At the highest point, the velocity of the ball is zero however the ball is still under the influence of gravity, here the acceleration due to gravity is acting downwards on the ball.
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in gel electrophoresis, dna fragments migrate toward the negative pole of the electric field. t/f
Answers
The given statement is true.
In gel electrophoresis, an electric field is applied to a gel matrix containing charged molecules such as DNA fragments. The electric field exerts a force on the charged molecules, causing them to migrate through the gel matrix.The DNA fragments are negatively charged due to the phosphate groups in their structure, and as a result, they migrate toward the positive pole of the electric field. However, since the gel electrophoresis apparatus is designed such that the negative electrode (cathode) is placed at the bottom of the gel, and the positive electrode (anode) is placed at the top, the DNA fragments move toward the negative pole. This is because the negatively charged molecules are attracted to the positively charged anode at the top of the gel, and move away from the negatively charged cathode at the bottom.To know more about electric field visit:
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Which three statements could explain the increase in the deer population? A. Rainfall was above average over the past five years B. A hawk species settled into the area five years ago C. Extremely harsh winters occurred during the past five years D. The number of cattle ranchers decreased in the past five years E. The law allowed an extended wolf hunting season for the past five years
Answers
Answer:
D. The number of cattle ranchers decreased in the past five years
Explanation:
According to Jennifer M Schieltz and Daniel I Rubenstein (2016), "More than a quarter of earth's land surface is used for grazing domestic livestock." This has negative effects on availability of pasture for herbivorous wildlife such as the deer.
Increase in the number of cattle ranchers decreases the availability of pasture and vice versa.
Hence, the decrease in the number of cattle ranchers over the past five years led to an increase in the deer population due to a decrease in competition for pasture.
Which of the following combinations would result in the least acceleration?
O SN and 0.35 kg
60N and 2.0 kg
O 12N and 1.0 kg
O IN and 0.20 kg
Answers
The lowest-intensity sound that is still audible has an intensity of approximately I= 10^-12 W/m^2. Consider a jet that flies at an altitude of 6,500 m. Estimate the smallest the sound power output of the airplane engine could be so that it could still be heard on the ground.
Answers
The smallest sound power output of the airplane motor that can be listened to on the ground is 6.73 × 10^-6 W which has the lowest-intensity sound that is still loud and has an intensity of 10^-12 W/m^2.
The intensity of sound = 10^-12 W/m^2
Altitude = 6,500 m.
Calculate the smallest sound energy output of an aircraft motor that can be heard on the ground is done by using the formula:
I = P/(4πr^2)
Pythagoras' theorem is used for calculating the distance
d = (\(\sqrt{6500^2 + R^2}\))
I = 10^-12 W/m^2
d = \(\sqrt{6500^2 + R^2}\)
d = 6500 m
P/(4πd^2) = I
\(P/(4π(6500)^2) = 10^-12 W/m^2\)
\(P = 4π(6500)^2 × 10^-12 W\)
P = 6.73 × 10^-6 W
Therefore, we can conclude that the smallest sound power output of the aircraft engine that can be heard on the ground is 6.73 × 10^-6 W.
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What are 5 different ways to use a fidget spinner?
Answers
Answer:
Balancing on one finger.
Tossing between hands.
Using a different body part.
Building a tower.
Throwing it high in the air.
Flipping it over.
Switching between fingers.
Going behind the back.
Explanation:
Just stuff I used to do ^^
Which statement about the dark nebulae is true? Group of answer choices They can be penetrated only with longer wavelengths such as radio and infrared. They block the vast majority of radio waves from our Galaxy. Hydrogen and helium are the chief absorbing and scattering agents. They can be penetrated only with shorter waves, such as UV and x-ray. Only one is known to exist.
Answers
Answer:
They can be penetrated only with longer wavelengths such as radio and infrared.
Explanation:
A dark nebula can be defined as an interstellar cloud that is so dense as a result of high concentration of gas and dust and as such it obscures the visible wavelengths of light from stars behind it, thus appearing completely opaque (dark patch) in front of a bright emission nebula or in regions having plenty stars.
Hence, dark nebulae can be penetrated only with longer wavelengths such as radio and infrared light because they cannot be absorbed by the dust layers or particles coated with frozen carbon monoxide and nitrogen residing in the dark nebulae.
5. This break-dancer's speed is not changing as he spins on his head, but he is
accelerating. Explain how this could be.
Answers
The direction of the break dancer is always changing hence we can say that the break dancer is accelerating.
The term acceleration means change of velocity with time. It refers to the time taken for the velocity of a body to change in a specified direction. Recall that velocity takes direction into account.
The direction of the break dancer is always changing hence we can say that the break dancer is accelerating since his direction is changing even though the speed is constant.
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The Integrated circuit (microelectronic circuit on a chip) was first invented/developed in 1958 with milli-meter (1/1000 of a meter) device dimensions. Today, integrated circuits use 5 nano-meter (5/1000,000,000 of a meter) device dimensions. What have been the implications on computing and communications resulting from this million times shrinking of device dimensions over the past 6 decades. Be specific, like the impact on speed of computing, and sophistication of circuit functions, etc. 20 points
Answers
The shrinking of integrated circuit device dimensions over six decades led to faster computing, advanced circuit functions, improved power efficiency, and widespread advanced electronic devices.
Increased Computing Speed: As device dimensions have shrunk, the distance between transistors on a chip has decreased, enabling faster electrical signal propagation. This has led to increased clock speeds and faster processing capabilities, allowing for more complex computations and faster data processing.
Enhanced Circuit Functionality: With smaller device dimensions, more transistors can be integrated into a single chip. This has enabled the development of highly sophisticated and complex circuits, such as microprocessors, capable of performing intricate tasks.
The increased number of transistors has also facilitated the integration of various functionalities, such as memory, graphics processing, and communication capabilities, onto a single chip, leading to more versatile and powerful computing devices.
Improved Power Efficiency: Smaller device dimensions have reduced the distance that electrical signals need to travel within a chip. This has minimized the power losses associated with signal propagation, resulting in improved power efficiency. Additionally, the miniaturization of components has allowed for the development of low-power transistors, enabling energy-efficient operation and longer battery life in portable electronic devices.
Proliferation of Advanced Electronic Devices: The million-fold reduction in device dimensions has made it possible to produce smaller, lighter, and more compact electronic devices. This has led to the widespread adoption of smartphones, tablets, wearables, and other portable devices that offer advanced computing, communication, and multimedia capabilities. The miniaturization of integrated circuits has also enabled the development of Internet of Things (IoT) devices, smart sensors, and embedded systems, which have revolutionized various industries and aspects of everyday life.
Increased Integration and System Complexity: Shrinking device dimensions have allowed for greater integration of components and systems on a single chip. This has led to the development of system-on-chip (SoC) solutions, where multiple functions, such as processing, memory, and communication, are combined on a single integrated circuit. The increased integration and system complexity have contributed to the advancement of technologies like artificial intelligence, machine learning, and autonomous systems.
Cost Reduction: The continual shrinking of device dimensions has resulted in increased transistor density on a chip. This has led to higher production yields per wafer, driving down the manufacturing cost per transistor. The cost reduction has made advanced computing and communication technologies more affordable and accessible to a wider range of users, fostering their widespread adoption.
Overall, the million times shrinking of device dimensions in integrated circuits over the past six decades has had a profound impact on computing and communications, revolutionizing the speed, functionality, power efficiency, and size of electronic devices while enabling the development of new technologies and driving economic growth in the digital era.
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Psertica track detectors are ised to measure the speed of particles in the lifetime of the particie is known. Particie-X has a lifetime of 256.2. an experment inside the detector by a given reaction. The partides leave 10.6 cm long tracks on average before they decay into other particies not abservable by the detectori What is the aunage speed of the particles in terms of the speed of light? Tries 0/12
Answers
The average speed of the particles in terms of the speed of light is 0.976c. Given that, The particle-X has a lifetime of 256.2.A particle track detector is used to measure the speed of particles. On average, the particles leave 10.6 cm long tracks before they decay into other particles that are not observable by the detector.
The formula to calculate the average speed of the particles is given as;v = d / t Where,v = velocity of the particles, d = distance traveled by the particles, and t = time taken by the particles. The distance traveled by the particles before they decay is 10.6 cm = 0.106 m. The lifetime of the particle is given as 256.2 s. Therefore, time taken by the particle to decay, t = 256.2 s.
The speed of the particles can be calculated as follows; v = d / tv = 0.106 / 256.2v = 4.135 × 10^-4 m/s The speed of the particles in terms of the speed of light can be calculated as follows; Speed of light = 3 × 10^8 m/s Average speed of the particles in terms of the speed of light, v/c= (4.135 × 10^-4) / (3 × 10^8)= 0.976 × 10^-8= 0.976cTherefore, the average speed of the particles in terms of the speed of light is 0.976c.
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What do you observe as you immerse the empty jug in a bucket which contains water? Explain why you observe this phenomenon.
Answers
Answer:
The jug drowns because the density of the jug is more than that of the density of water.
Answer:
it gets force upwards .
as there is presence of atmospheric pressure in it which causes upthrust and push upwards.
characteristics of radiation from the sun's energy would be
A. heat from a distance source, elcetromagnatic waves and energy that travels through space.
B. Direct contact of the energy source of sufaces
C. Movement of heat through fluids
WHICH ONE IS THE ANSWER HELPPP
Answers
Answer:
Answer is A
Explanation:
a factory has a machine which bends wire at a rate of 4 unit(s) of curvature per second. how long does it take to bend a straight wire into a circle of radius 1?
Answers
It will take approximately 1.57 seconds to bend the straight wire into a circle of radius 1 using the machine that bends wire at a rate of 4 units of curvature per second.
To identify how long it takes to bend a straight wire into a circle of radius 1 using a machine that bends wire at a rate of 4 units of curvature per second, we need to consider a few key factors.
First, we should note that the wire needs to be bent into a complete circle, which means it needs to form a 360-degree curve. Since the machine bends wire at a rate of 4 units of curvature per second, it will take 360/4 = 90 seconds to complete one full revolution.
Now, let's calculate the time it takes to bend the straight wire into a circle of radius 1. The circumference of a circle with a radius of 1 is 2π (approximately 6.28). Since the machine bends wire at a rate of 4 units of curvature per second, it will take 6.28/4 = 1.57 seconds to bend the wire into a circle of radius 1.
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Banana slugs move at a slow pace of 0.5 feet per minute. After an hour, a banana slug can move feet.
Answers
Study the distance-time graph, showing the distances that eight different things cover in 120 seconds or less. The letters below correspond to the lines on the graph. For each object, calculate the average speed, and then match it with the closest correct answer.
A:
B:
C:
D:
E:
F:
G:
H:
Answers
Answer:
This question appear incomplete
Explanation:
This question appear incomplete because there is no list of closest correct answer there. Although can still be well attempted.
The formula to be used here is
average speed = distance ÷ time
The unit of speed here would be meters per second (m/s). However, some of the lines do not really fall on a measurable line on the graph and can only be "best assumed".
A: distance is 1600 meters
time appear to be 4 seconds (definitely less than 5 seconds according to the graph).
speed = 1600 ÷ 4
speed = 400 m/s
B: distance is 1600 meters
time appear to be 18 seconds (definitely less than 20 seconds according to the graph)
speed = 1600 ÷ 18
speed = 88.89 m/s
C: distance is 1600 meters
time is 65 seconds
speed = 1600 ÷ 65
speed = 24.62 m/s
D: distance is 1600 meters
time is 105 seconds
speed = 1600 ÷ 105
speed = 15.24 m/s
E: distance is 1100 meters
time is 120 seconds
speed = 1100 ÷ 120
speed = 9.17 m/s
F: distance is 500 meters
time is 120 seconds
speed = 500 ÷ 120
speed = 4.17 m/s
G: distance appear to be 250 meters
time is 120 seconds
speed = 250 ÷ 120
speed = 2.08 m/s
H: distance appear to be 50 meters
time is 120 seconds
speed = 50 ÷ 120
speed = 0.42 m/s
The average speed for each object are:
1. The average speed of A is 400 m/s
2. The average speed of B is 88.89 m/s
3. The average speed of C is 24.62 m/s
4. The average speed of D is 15.24 m/s
5. The average speed of E is 9.17 m/s
6. The average speed of F is 4.17 m/s
7. The average speed of G is 2.08 m/s
8. The average speed of H is 0.33 m/s
Average speed is defined as the total distance travelled divided by the total time taken to cover the distance.
Average speed = Total distance / total timeWith the above formula, we can obtain the average speed for each object as follow:
1. Determination of average speed of A
Total distance = 1600
Total time = 4 s
Average speed =?Average speed = 1600 / 4
Average speed of A = 400 m/s2. Determination of average speed of B
Total distance = 1600
Total time = 18 s
Average speed =?Average speed = 1600 / 18
Average speed of B = 88.89 m/s3. Determination of average speed of C
Total distance = 1600
Total time = 65 s
Average speed =?Average speed = 1600 / 65
Average speed of C = 24.62 m/s4. Determination of average speed of D
Total distance = 1600
Total time = 105 s
Average speed =?Average speed = 1600 / 105
Average speed of D = 15.24 m/s5. Determination of average speed of E
Total distance = 1100
Total time = 120 s
Average speed =?Average speed = 1100 / 120
Average speed of E = 9.17 m/s6. Determination of average speed of F
Total distance = 500
Total time = 120 s
Average speed =?Average speed = 500 / 120
Average speed of F = 4.17 m/s7. Determination of average speed of G
Total distance = 250
Total time = 120 s
Average speed =?Average speed = 250 / 120
Average speed of G = 2.08 m/s8. Determination of average speed of H
Total distance = 40
Total time = 120 s
Average speed =?Average speed = 40 / 120
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Cadmium has eight naturally occurring isotopes. What do the isotopes have in common?
A.
atomic mass
B.
mass number
C.
number of protons
D.
number of neutrons
Answers
The isotopes of any element have same number of protons inside them.
What is Cadmium?Cadmium is a chemical element with the symbol Cd and atomic number 48. It is soft, silvery and white metal.
Given is about Cadmium that it has eight naturally occurring isotopes.
Isotopes are the atoms of the same element which have same number of protons in them but the number of neutrons are different. Isotopes usually have same chemical properties, but they have different physical properties. Their can be stable and unstable isotopes. These unstable isotopes are also called radioisotopes, since they emit radiation. Thus, the isotopes have same number of protons.
Therefore, the isotopes of any element have same number of protons inside them.
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A roll of toilet paper is dropped from a height of 1. 8 m. Another one is dropped at the same time but someone holds the end of the roll so that it unwinds as it falls. From what height should the unwinding roll be released from so that it hits the floor at the same time as the one dropped from 1. 8m? tension force
Answers
The unwinding roll should be released from a height of 3.6m in order to hit the floor at the same time as the other roll.
When the roll of toilet paper is dropped from a height of 1.8 m, it experiences a gravitational force that accelerates it towards the ground. The acceleration experienced by the roll of toilet paper is equal to the acceleration due to gravity,
g = 9.8 m/s².
On the other hand, the roll of toilet paper that is unwinding experiences a tension force in addition to the gravitational force.
The tension force is caused by the frictional force between the roll and the toilet paper as it unwinds. This force acts upwards and opposes the gravitational force acting downwards. To determine the height from which the unwinding roll should be released, we need to equate the net force acting on it to the gravitational force acting on the other roll.
Let H be the height from which the unwinding roll is released. The net force acting on the unwinding roll is given by the tension force minus the gravitational force, which is:
T - mg
where T is the tension force, m is the mass of the roll and g is the acceleration due to gravity.
Since the two rolls are identical, m is the same for both rolls. The gravitational force acting on the other roll is simply mg. Equating the net force to the gravitational force and solving for H, we have:
T - mg = mg
T = 2mg
Using the formula for tension force in a hanging object, we can express T as:
T = mgh / L
where L is the length of the roll and h is the height from which it is released.
Substituting T = 2mg and solving for h, we obtain:
h = 2L
Therefore, the unwinding roll should be released from a height of
2L = 2(1.8m) = 3.6m
in order to hit the floor at the same time as the other roll.
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A fisherman rows a boat North directly across a river at 2m/s. The current of the river flows to East at 1.3m/s.
Represent the vectors for given situation graphically.
Answers
Here is a graphical representation of the vector pointing upwards represents the fisherman's velocity attached.
What are vectors?Vectors are mathematical objects used to represent quantities that have both magnitude and direction. They can be visualized as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.
Examples of quantities that can be represented as vectors include force, velocity, acceleration, and displacement. The vector pointing upwards represents the fisherman's velocity of 2 m/s towards the North, while the vector pointing towards the right represents the river's current of 1.3 m/s towards the East.
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The marble in the figure to the right has a mass of 3.75 g. When placed in a graduated cylinder, as pictured, the water level changes from 25 mL to 28 mL. What is the density of the marble?
Answers
Answer:
The answer is 1.25 g/mLExplanation:
The density of a substance can be found by using the formula
\(density = \frac{mass}{volume} \\\)
From the question
mass = 3.75 g
volume = final volume of water - initial volume of water
volume = 28 - 25 = 3 mL
We have
\(density = \frac{3.75}{3} \\ \)
We have the final answer as
1.25 g/mLHope this helps you
What will be the final velocity of a car, if it starts to move from rest and accelerates at 10 m/s² after 5 seconds ?
Answers
Answer:
50m/s.
Explanation:
Answer:
\(V_f=50m/s\)
Explanation:
Use the the formula for final velocity (kinematic equation):
\(V_f=V_i+at\)
Final velocity = Initial velocity + acceleration times time
Given values:
Rest - indicates 0 initial velocity
Acceleration - 10 m/s^2
Time - 5 seconds
Insert the given values:
\(V_f=0+5\times10\)
\(V_f=50m/s\)
A 63.0-kg sprinter starts a race with an acceleration of 3.20 m/s2. If the sprinter from the previous problem accelerates at that rate for 20.0 m, and then maintains that velocity for the remainder of the 100.0-m dash, what will be his time for the race
Answers
At his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.
What is velocity?
Velocity is a vector quantity that describes the rate of change of an object's position. It is a measure of how fast an object is moving and in what direction. Velocity is measured in units of meters per second (m/s) or miles per hour (mph) and is often represented by the symbol "v".
We can use the equations of motion to calculate the time for the sprinter to complete the race.
First, we can use the equation:
v = u + at
to find the final velocity of the sprinter after accelerating for 20.0 m. Here, u is the initial velocity (which is 0 m/s since the sprinter is at rest at the start of the race), a is the acceleration of 3.20 m/s^2, and t is the time it takes for the sprinter to accelerate for 20.0 m.
v = 0 + (3.20 m/s^2)(t)
We know that the sprinter accelerates for 20.0 m, so we can use the equation:
s = ut + 1/2at^2
to find the time t:
20.0 m = (0 m/s)(t) + 1/2(3.20 m/s^2)(t^2)
t^2 = (20.0 m) * 2 / (3.20 m/s^2) = 12.5
t = sqrt(12.5) = 3.53 s
So the time it takes for the sprinter to accelerate for 20.0 m is 3.53 s.
Next, we can use the equation:
v = d/t
to find the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity. Here, d is the remaining distance of 80.0 m and v is the final velocity found before.
t = d/v = 80.0 m / (3.20 m/s) = 25.0 s
So the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity is 25.0 s
So the total time for the race is the sum of the time it takes to accelerate and the time it takes to cover the remaining distance at a constant velocity:
t = 3.53 s + 25.0 s = 28.53 s
Hence, at his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.
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3. The mass of a density bottle is 20g when empty 70g when full of water and 695g when full of another liquid. Calculate the density of the other liquid (take density of water as 1g/cm²³ Mass of 20cm³ of the liquid (2mk) 4. The mass of a density bottle of volume 50cm3 is 10.0g when empty. Aluminium turnings are poured into the bottle and the total mass is 60.0g. Water is then added into the turnings till the bottle is fuil. If the total mass of the bottle and its contents is 90.0g, calculate the density of the aluminium turnings. (3mk) 5. An empty density bottle has a mass of 23g. When completely filled with water its mass is 39.0g. What will be its mass if it is completely filled with an acid of relative density 1.25? (Take the density of water as 1.0gcm-³)
Answers
The mass of the density bottle when completely filled with the acid of relative density 1.25 will be 71.75g.
To calculate the density of the other liquid, we can use the formula:
Density = (Mass of liquid - Mass of empty bottle) / Volume of liquid
Given:
Mass of empty bottle = 20g
Mass of bottle filled with water = 70g
Mass of bottle filled with the other liquid = 695g
Density of water = 1g/cm³
Volume of water = Mass of bottle filled with water - Mass of empty bottle = 70g - 20g = 50g
Density of the other liquid = (Mass of liquid - Mass of empty bottle) / Volume of liquid
= (695g - 20g) / 50cm³
= 675g / 50cm³
= 13.5g/cm³
Therefore, the density of the other liquid is 13.5g/cm³.
The question seems to be incomplete. Please provide additional information or clarify the given data to solve this problem.
To calculate the density of the aluminum turnings, we can use the formula:
Density = (Mass of turnings - Mass of empty bottle) / Volume of turnings
Given:
Volume of bottle = 50cm³
Mass of empty bottle = 10.0g
Total mass of bottle and contents = 90.0g
Mass of turnings = Total mass of bottle and contents - Mass of empty bottle
= 90.0g - 10.0g
= 80.0g
Density of aluminum turnings = (Mass of turnings - Mass of empty bottle) / Volume of turnings
= (80.0g - 10.0g) / 50cm³
= 70.0g / 50cm³
= 1.4g/cm³
Therefore, the density of the aluminum turnings is 1.4g/cm³.
To calculate the mass of the density bottle when filled with an acid of relative density 1.25, we can use the following formula:
Mass of filled bottle = Mass of empty bottle + (Relative density of acid * Mass of water)
Given:
Mass of empty bottle = 23g
Mass of water when bottle is completely filled = 39.0g
Relative density of acid = 1.25
Density of water = 1.0g/cm³
Mass of filled bottle = Mass of empty bottle + (Relative density of acid * Mass of water)
= 23g + (1.25 * 39.0g)
= 23g + 48.75g
= 71.75g
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