(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>
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(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>
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(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.
Answer:
1 million dollars once
Explanation:
Well, both would be nice. In total, you will get more from the million dollars because it takes over 2,739 years to get 1 million dollars worth of pennies.(if you get 1 a day that is)
Answer:
option B
Explanation:
given,
diameter of the rotating space = 2 Km
Force exerted at the edge of the space = 1 g
force experienced at the half way = ?
As the object is rotating in the circular part
Force is equal to centripetal acceleration.
at the edge
g = ω² r
ω is the angular velocity of the particle
r is the radius.
now, acceleration at the half way
g' = ω² r'



People at the halfway experience g/2
hence, the correct answer is option B
Question:
1) The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.
2) The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.
3) The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.
4) The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.
Answer:
The correct option is;
3) The Universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses
Explanation:
With the temperature measurement carried out using the CSIRO radio telescope, Astronomers have been able to determine a temperature difference in the universe from 5.08 Kelvin 7.2 billion light years away to 2.73 Kelvin in the Universe today, which is in support of the Big Bang theory that as the Universe expanded from a state of extreme temperature that cools down as the Universe expands or the cosmos disperses.