(a) Differentiate the position vector to get the velocity vector:
<em>r</em><em>(t)</em> = (3.00 m/s) <em>t</em> <em>i</em> - (4.00 m/s²) <em>t</em>² <em>j</em> + (2.00 m) <em>k</em>
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em> = (3.00 m/s) <em>i</em> - (8.00 m/s²) <em>t</em> <em>j</em>
<em></em>
(b) The velocity at <em>t</em> = 2.00 s is
<em>v</em> (2.00 s) = (3.00 m/s) <em>i</em> - (16.0 m/s) <em>j</em>
<em></em>
(c) Compute the electron's position at <em>t</em> = 2.00 s:
<em>r</em> (2.00 s) = (6.00 m) <em>i</em> - (16.0 m) <em>j</em> + (2.00 m) <em>k</em>
The electron's distance from the origin at <em>t</em> = 2.00 is the magnitude of this vector:
||<em>r</em> (2.00 s)|| = √((6.00 m)² + (-16.0 m)² + (2.00 m)²) = 2 √74 m ≈ 17.2 m
(d) In the <em>x</em>-<em>y</em> plane, the velocity vector at <em>t</em> = 2.00 s makes an angle <em>θ</em> with the positive <em>x</em>-axis such that
tan(<em>θ</em>) = (-16.0 m/s) / (3.00 m/s) ==> <em>θ</em> ≈ -79.4º
or an angle of about 360º + <em>θ</em> ≈ 281º in the counter-clockwise direction.
The scientific question can be supported by evidence that must be true of the possible answers to a scientific question. Option D is correct,
<h3>What is a Scientific hypothesis?</h3>
A scientific hypothesis must meet two criteria, A scientific hypothesis must be testable, and a scientific hypothesis must be falsifiable The basic idea of a hypothesis is that there is no predetermined outcome.
For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation.
Only scientific questions may be answered by scientific activity. The design of the research is also influenced by scientific issues.
The scientific question can be supported by evidence that must be true of the possible answers to a scientific question.
They are accurate regarding the scientific question and can be substantiated by proof.
Hence option D is correct.
To learn more about the hypotheses refer to the link ;
https://brainly.in/question/1769011
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Answer:
an air mass is a volume of air defined by its temperature and water vapor content. Air masses cover many hundreds or thousands of miles, and adapt to the characteristics of the surface below them. They are classified according to latitude and their continental or maritime source regions. Colder air masses are termed polar or arctic, while warmer air masses are deemed tropical. Continental and superior air masses are dry while maritime and monsoon air masses are moist. Weather fronts separate air masses with different density (temperature and/or moisture) characteristics. Once an air mass moves away from its source region, underlying vegetation and water bodies can quickly modify its character.When winds move air masses, they carry their weather conditions (heat or cold, dry or moist) from the source region to a new region. When the air mass reaches a new region, it might clash with another air mass that has a different temperature and humidity. This can create a severe storm.
Air masses can affect the weather because of different air masses that are different in temperature, density, and moisture. When two different air masses meet a front forms. This is one way air masses effect our weather.
348.34 m/s. When Superman reaches the train, his final velocity will be 348.34 m/s.
To solve this problem, we are going to use the kinematics equations for constant aceleration. The key for this problem are the equations
and
where
is distance,
is the initial velocity,
is the final velocity,
is time, and
is aceleration.
Superman's initial velocity is
, and he will have to cover a distance d = 850m in a time t = 4.22s. Since we know
,
and
, we have to find the aceleration
in order to find
.
From the equation
we have to clear
, getting the equation as follows:
.
Substituting the values:

To find
we use the equation
.
Substituting the values:

Force applied by the machine to over come resistance