what is the shortest possible time in which a bacterium could travel a distence of 8.4 cm across a petri dish at a constant speed of 3.5mm

The difference in height between both players, Arabella and Boris, is given by [tex]D(t) = h_A(t) - h_B (t)[/tex]

This problem is a 1-dimensional free fall type of problem, it's one dimensional since both players only move in 1 dimension (meaning vertically), and it is a free fall problem since, when both players leave the ground, the only force which is apllied over them is the force excerted by gravity.

To solve our problem, let's suppose that both players jump from a point called the origin, meaning a point where we consider that their vertical displacement is 0 (in this case, the floor would be considered as the origin). Besides that, let's suppose that we start counting the time at the moment when Arabella makes her jump, and let's say that both players jump with velocity V. Therefor from the equations from kinematics about free falling objects we can write an expression for the height of Arabella over time as:

[tex]h_A (t) = V \cdot t - \frac{g \cdot t^2}{2}[/tex]

Which is an equation valid since the time Arabella jumps until she gets back on the ground, in math terms this would be written as that the equation is valid over the interval [tex]0\leq t\leq \frac{2 \cdot V}{g}[/tex]. At all other times the height of Arabella would be zero (since she is on the ground).

We can write the same for Boris, though his equation is shifted in time by his reaction time [tex]t_r[/tex]:

[tex]h_B (t) = V \cdot (t-t_r) - \frac{g \cdot (t-t_r)^2}{2}[/tex]

Which is valid over the interval [tex]t_r \leq t\leq t_r + \frac{2 \cdot V}{g}[/tex], and zero everywhere else (since Boris is touching the ground at all other moments). Putting all the pieces together, we can get a piecewise function that expresses the difference in height between both players:

[tex]D(t) = h_A(t) - h_B (t) = V \cdot t - \frac{g \cdot t^2}{2} [/tex] for all [tex]0 \leq t \leq t_r[/tex]

[tex]D(t) = h_A(t) - h_B (t) = V \cdot t - \frac{g \cdot t^2}{2} - (V \cdot (t-t_r) - \frac{g \cdot (t-t_r)^2}{2}) =  V \cdot t_r - g \cdot t_r \cdot t + \frac{g \cdot t_r^2}{2} [/tex] for all [tex]t_r \leq t \leq \frac{2 \cdot V}{g}[/tex]

[tex]D(t) = h_A(t) - h_B (t) = - V \cdot (t-t_r) + \frac{g \cdot (t-t_r)^2}{2} [/tex] for all [tex]\frac{2 \cdot V}{g} \leq t \leq t_r + \frac{2 \cdot V}{g}[/tex]

Here is a list of well explained free falling problems, similar to yours:

Free fall, parabolic motion, kinematics

Vertical displacement when [tex]t=t_r[/tex] is [tex]\b{\boxed{\sqrt{2gH}\left(t\right)-\dfrac{1}{2}g{t^2}}}[/tex] and vertical displacement when [tex]{t_r}<t[/tex] is [tex]\b{\fbox{\begin\{t({\sqrt{2gH}+\dfrac{g(t_r-2t)}{2})}\end{minispace}}}[/tex].

Further Explanation:

Arabella and Boris are of same height and jumps with the same initial velocity. Therefore, both can jump to height [tex]H[/tex].

The energy of both the players Arabella and Boris at ground level and height [tex]H[/tex] is constant.

Concept:

Applying conservation of energy at ground and height [tex]H[/tex]:

[tex]mgH=\dfrac{1}{2}m{v_0}^2[/tex]

Rearrange the above equation for initial velocity [tex]v_0[/tex]:

[tex]v_0=\sqrt{2gH}[/tex]

To calculate the height of both players, we can apply the equation of law of motion.

For a given initial velocity [tex]v_0[/tex], acceleration [tex]g[/tex], the height of the Arabella in time [tex]t[/tex]:

[tex]\boxed{{h_a}\left(t\right) ={h_0}+{v_0}t-\dfrac{1}{2}g{t^2}}[/tex]

The reaction time for Boris is [tex]t_r[/tex]. Therefore, to reach the height time taken by her is [tex](t-t_r)[/tex] .

For a given initial velocity [tex]v_0[/tex], acceleration [tex]g[/tex], the height of the Boris in time [tex](t-t_r)[/tex]:

[tex]\boxed{{h_b}(t)={h_0}+{v_0}(t-t_r)+\dfrac{1}{2}g(t-t_r)^2}[/tex]

It is given that Boris jumps before Arabella reaches the maximum height. Therefore, reaction time for Boris cannot be greater than total time.

Case I:

For [tex]t=t_r[/tex], we get [tex]{h_b}(t)={h_0}[/tex] .

Therefore, the vertical displacement is:

[tex]\begin{aligned}D(t)&={h_a}(t)-{h_b}(t)\\&={h_0}+{v_0}t-\dfrac{1}{2}g{t^2}-{h_0}\\&={v_o}t-\dfrac{1}{2}g{t^2}\\&=\sqrt{2gH}(t)-\dfrac{1}{2}g{t^2}\end{gathered}[/tex]

Case II:

For [tex]{t_r}<t[/tex], the vertical displacement is:

[tex]\begin{aligned}D(t)&={h_a}(t)-{h_b}(t)\\&={t_r}({\sqrt{2gH}+\dfrac{g(t_r-2t}{2})\end{aligned}[/tex]  

Thus, vertical displacement when [tex]t=t_r[/tex] is [tex]\b{\boxed{\sqrt{2gH}\left(t\right)-\dfrac{1}{2}g{t^2}}}[/tex] and vertical displacement when [tex]{t_r}<t[/tex] is [tex]\b{\fbox{\begin\{t({\sqrt{2gH}+\dfrac{g(t_r-2t)}{2})}\end{minispace}}}[/tex].

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords:

Two, basketball, player, same, height, initial, velocity, vertical, distance, Arabella, Boris, high, above, D(t)=Ha(t) – Hb(t), function, reaction, ground, reaches and time.

Answer:

C is the answer

Answer:

Mathematically, the acceleration of a body at any time is the second derivative of the position:

[tex]a=\frac{d^2x}{dt^2}[/tex]

In addition, it can be obtained by deriving the speed of the body:

[tex]a=\frac{dv}{dt}[/tex]

Explanation:

In classical mechanics acceleration is defined as the variation of speed with respect to time:

[tex]a=\frac{dv}{dt}[/tex]

In Newtonian mechanics, for a body with constant mass, the acceleration of the body measured by an inertial observer is proportional to the force acting on it:

[tex]F=ma\\\\a=\frac{F}{m}[/tex]

A SULFATE  IS THE CORRECT ANSWER

Answer:

Erosion is the constant gnawing, erosion and degradation that occurs on the earth's surface. That is, when external geological forces, such as rivers, glaciers, flowing water, winds or waves, carry along and gnaw rock particles and move material from one location on the earth's surface to another.

The rate of erosion is influenced by climate, topography, the extent of vegetation cover and the properties of the loads. Deforestation and cultivation methods that change the soil structure, for example, make the soil harder so that it does not drain away water so quickly, can increase the erosion rate and cause major damage. It is estimated that 30-40 billion tonnes of land is eroded each year from the world's agricultural areas.

Answer:

A teaspoon

Explanation:

As we know that the capacity of hold something by a standard teaspoon is related with milliliters as,

1 teaspoon is equivalent to 4.92892 milliliters

From this it can be see that the 1 teaspoon is equivalent to approximately 5 milliliters.

Therefore, the water hold by 1 teaspoon is more than the water hold by a milliliter.

Joe will take approximately 738.33 seconds to climb from street level to the roof of the Sears Tower.

To calculate the time it will take Joe to climb from street level to the roof of the Sears Tower, we can use the formula:

Time = Distance/Speed

Joe is climbing a distance of 443 m at an average speed of 0.60 m/s, so we can substitute these values into the formula:

Time = 443 m / 0.60 m/s = 738.33 s

Therefore, it will take Joe approximately 738.33 seconds to climb from street level to the roof of the Sears Tower.

Answer:

Acceleration, [tex]a=-83.33\ m/s^2[/tex]

Explanation:

It is given that,

Initial speed of the satellite, u = 10000 m/s

Final speed of the satellite, v = 5000 m/s

Time taken, t = 1 min = 60 seconds

Acceleration of the satellite is given by :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{5000-10000}{60}[/tex]

[tex]a=-83.33\ m/s^2[/tex]

So, the acceleration of the pumpkin is [tex]-83.33\ m/s^2[/tex]. Hence, this is the required solution.

it is B.

Yes, the force applied is parallel to the direction of motion

Answer:

The answer is: "Yes, the force applied is parallel to the direction of motion" Hope this helps :)

Explanation:

Coaxial cables offer a potential data transfer rate of 80 times quicker than twisted pair connections, which have a maximum of 10 Mbps. High-speed data transport occurs using optical fiber lines. About 69% of the speed of light is used to describe the transfer speed.

An assemblage of one or more wires running parallel to one another or bundled together that is used to transport electric current is known as an electrical cable.

A cable assembly, which is not always appropriate for connecting two devices but can be a partial product, can be made up of one or more electrical cables and the necessary connectors. A cable tree or cable harness are other examples of cable assemblies that can be utilized to link numerous terminals.

One or more optical fibers are used to carry data using fiber optic cables, also known as optical fiber cables, a type of Ethernet cable. As light pulses pass through small glass tubes, fiber optic cable transfers data. Twisted pair cable's transmission capacity is 26,000 times lower than optical fiber cable's transmission capacity.

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Final answer:

Fiber optic cables, twisted pair cables, and coaxial cables are different types of cables used in telecommunications. Fiber optic cables use light signals for data transmission, while twisted pair and coaxial cables use electrical signals. Each cable has its own advantages and is used for different purposes.

Explanation:

Fiber optic cables, twisted pair cables, and coaxial cables are all types of cables used for transmitting signals in telecommunications. Here are the differences:

Overall, the choice of cable depends on the specific application and requirements.

The part of the ignition system that amplifies the electric voltage is the coil as it is described to be something that is joined in a shape of a spiral or rings in a specific machine or vehicle, amplifying electricity.

Answer : Gravity

Explanation :  Matter comes together to form stars under the force of gravity. Gravity is a force that causes all object to attract each other . This force dependent on their masses and their distance.

So, we can say that scientist know the force of gravity is responsible for clumping matter together to form the first stars after the big bang.

Final answer:

Work involves a force causing a displacement, and power is the rate at which work is done over time. The correct answer is A. work involves force and distance while power involves force and velocity.

Explanation:

Work and power are different concepts within physics. The difference between them is that work involves a force causing a displacement, while power is the rate at which work is done over time. Specifically, work done (W) is calculated as the product of force (F) and displacement (d) in the direction of the force: W = Fd. Power (P) is the rate at which this work is done, which is work divided by the time (t) it takes to do the work: P = W/t.

Therefore, the correct answer to the student's question is:

A. work involves force and distance while power involves force and velocity.

For light or ultraviolet, the formula for energy can be calculated using Planck’s equation. That is:

E =  h c / ʎ

where,

h is the Planck’s constant = 6.626 * 10^-34 m^2 kg / s

c is the speed of light = 3 * 10^8 m/s

ʎ is the wavelength of light = 110 nm = 110 x 10^-9 m

So calculating for energy E:

E = (6.626 * 10^-34 m^2 kg / s) * (3 * 10^8 m/s) / (110 x 10^-9 m)

E = 1.807 x 10^-18 J

It is A. Im taking the test right now.

Answer :(A) Velocity on the y-axis, time on the x-axis

Explanation :

It is given that, Larry and Balky started the marble at the top of the ramp and set up photogates to collect data as the marble rolled down the ramp.

Acceleration is defined as the rate of change of velocity.

Instantaneous acceleration is defined as the slope of the tangent line. It is also defined as the rate of change of velocity at a particular instant.

To find instantaneous acceleration, it should be a velocity - time graph with velocity on the y-axis and time on the x-axis.

So, the correct option is (A) "Velocity on the y-axis, time on the x-axis".

Answer : Distance covered is 220 miles.

Explanation :

It is given that,

Speed of Marcus's Honda Prelude, [tex]v=55\ miles/hour[/tex]

Time duration, [tex]t=4\ hours[/tex]

We know that the speed of an object is defined as the distance travelled per unit time.

[tex]v=\dfrac{d}{t}[/tex]

or

[tex]d=v\times t[/tex]

[tex]d=55\ miles/hour\times 4\ hours[/tex]

[tex]d=220\ miles[/tex]

Hence, this is the required solution.      

There is a simple pattern for determining if a binary number is odd. This is when the number ends in 1. This pattern occured because they are defined by an odd word.

The binary number is a number that expressed in the base-2 numeral system or binary numeral system, that uses only two symbols, typically "0" and "1".

If the number ends in 1, it will be odd, whereas if the number ends in 0, it's even. Because the first digit can only be 0 or 1, the rest of the digits are multiplied by two.  To convert a binary number to base 2k, split it into groups of k digits by adding leading 0s if necessary, then convert each group to base 2k.

Example:

This pattern odd occured because they are defined by an odd word.They are numbers, that are by definition is too many things that they become odd, and also because they look odd again even when split into two

Grade:  9

Subject:  physics

Chapter:  Computer Science

Keywords: binary number, pattern, odd binary number, even binary number, Computer Science

At the edge of the cliff, the speed of the car will have two components. The x-component, horizontal, is equal to 27 m/s while the y-component, vertical, is equal to zero. With this, the car is seemingly in free-fall.

 The equation that would allow us to answer the question above is,

    d = (V₀)t + 0.5gt²

where d is distance, V₀ is the initial velocity, g is the acceleration due to gravity and t is the time. Substituting the known values,

    73 = (0)(t) + 0.5(9.8 m/s²)(t²)

Vo  equals zero because we only consider the y-component of the vector. Solving for the value of t will give us an answer of 3.86 s.

Answer: 3.86 seconds

To calculate the time it takes for the car to hit the ground when driving horizontally off a cliff, you can use the equation of motion for vertical motion and solve for time. The equation is y = yo + vot + 1/2at^2, where yo is the initial vertical position, vo is the initial vertical velocity, a is the acceleration due to gravity, and t is the time taken. Plug in the given values and solve for t.

To calculate the time it takes for the car to hit the ground, we can use the equation of motion for vertical motion: y = yo + vot + 1/2at^2. Since the car is driving horizontally, the initial vertical velocity vo is equal to zero, and the initial vertical position yo is equal to the height of the cliff, which is 73 meters. The acceleration due to gravity a is approximately -9.8 m/s^2 (negative because it acts in the opposite direction of the car's motion). Plugging in these values, we get:

y = 73 + 0t - 1/2(9.8)t^2

We can solve this equation for t by setting y equal to zero (since the car hits the ground), and solving the resulting quadratic equation. The positive solution will give us the time it takes for the car to hit the ground.

Let me calculate that for you.

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Final answer:

One water molecule is lost for every glycosidic bond formed in the polysaccharide chain, meaning for N monosaccharides joined, N-1 water molecules are lost.

Explanation:

Rule for Water Molecules Lost in Polysaccharide Formation;

During the formation of polysaccharides from monosaccharides, a dehydration reaction occurs. This means for every glycosidic bond formed, one water molecule is released. Therefore, a simple rule to determine the number of water molecules lost is as follows: for N monosaccharides joined to form a polysaccharide, the number of water molecules lost would be N-1. If two monosaccharides join to form a disaccharide, one water molecule is lost; if three join to form a trisaccharide, two are lost, and so on.

To illustrate, if you have 10 monosaccharides combining, you would lose 9 water molecules in the process, as 10-1=9. This reaction can be reversed through hydrolysis, where adding water can break the glycosidic bonds, converting the polysaccharide back into individual monosaccharides.

Answer:

Two essential measurements to calculating average speed are distance and time.