(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 type of pipe wrenches which are designed to turn and hold where marring is not objectionable is known as the chain wrench.<span> It has two serrated which adjust and grip the pipe. </span>
The kinetic energy in the first case is 4 times more than the second case.
Hence, option D)It is 4 times greater is the correct answer.
<h3>What is Kinetic Energy?</h3>
Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Given that;
- For the first case, velocity v = 16m/s
- For the second case, velocity = 8m/s
- Let the mass of the car be m
For the first case, kinetic energy of the car will be;
K = (1/2)mv²
K = (1/2) × m × (16m/s)²
K = (1/2) × m × 256m²/s²
K = mass × 128m²/s²
For the second case, kinetic energy of the car will be;
K = (1/2)mv²
K = (1/2) × m × (8m/s)²
K = (1/2) × m × 64m²/s²
K = mass × 32m²/s²
Comparing the kinetic energy of the car with the same mass but different velocity, we can see that the kinetic energy in the first case is 4 times more than the second case.
Hence, option D)It is 4 times greater is the correct answer.
Learn more about kinetic energy here: brainly.com/question/12669551
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Of the cliff?
Projectile motion
In the problem we are asked to find a height of certain cliff when a motorcycle stunt driver zoom out horizontally at the end the cliff at an initial velocity. So we will use one of the kinematics equation for projectile motion,
y
=
v
o
y
t
+
1
2
g
t
where
v
o
y
is just equal to zero since we can assume that the driver zooms out horizontally,
g
=
9.8
m
/
s
2
and
t
is time after
Answer:
16200 J
Explanation:
t = Time the battery is on = 60 hours
I = Current = 
Average voltage
Energy is given by
The energy delivered in the given time is 16200 J
