(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:
d) is the same as when it started from rest
Explanation:
using equation of motion
v = u + at
second law of momentum defines
F = ma
a = F /m
the equation becomes
v = u + (F/m)t
from hear
since v is directly proportional to the force and the force remain the same, the increase in the cart speed will also remain the same.
Answer:
(a) 
(b) 
Explanation:
Part (a)
The total length of copper cord L=86.3 m
The cross sectional area A=1.71×10⁻⁶m²
The resistivity of copper p=1.72×10⁻⁸Ω
Thus the resistance of extension cord is
Part (b)
The resistance of trimmer Rt=17.9 ohms
When voltage of 120V is applied then the current I is passing through series circuit is
Thus the voltage across the trimmer is:
Answer:
1900 meters
Explanation:
30m/s x 30 second = 900 meters
+ 1000 meters starting position
= 1900meters
As one moves farther and farther from the Sun, the distance between adjacent planets is greater.
