(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>
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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:
30 feet
Explanation:
First off, if they are throwing at 12.0 m/s and it takes 2.5 seconds. It will be the act of multiplication.
12 times 2.5 is 30, because 12 times 2 is 24 plus 12 divided by 2 which is 6 so 24 plus 6 is 30.
Answer:
D. power
Explanation:
kg represents mass
(m/v)² represents velocity squared
Then kg·m²/s² represents mass·velocity² = <em>kinetic energy</em> or <em>potential energy</em> or <em>work</em>.
kg·m²/s³ will be the <em>rate of doing work</em>, which is power
The cost of boiling 500 cm³ of water using the 3 KW Kettle is 1.35p
<h3>What is power? </h3>
This is defined as the rate in which energy is consumed. Electrical power is expressed mathematically as:
Power (P) = Energy (E) / time (t)
P = E / t
<h3>How to determine the energy</h3>
- Power (P) = 3 KW
- Time (t) = 3 mins = 3 / 60 = 0.05 h
- Energy (E) =?
E = Pt
E = 3 × 0.05
E = 0.15 KWh
<h3>How to determine the cost</h3>
- Energy (E) = 0.15 KWh
- Cost per unit = 9p
- Cost =?
Cost = Energy × cost per unit
Cost = 0.15 × 9
Cost = 1.35p
Learn more about electrical power:
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