(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.
Mass x SH x °C (or K) ΔT
= 75g x 0.45J/g/K x 6.0 ΔT
= 202.5 Joules of heat absorbed.
(202.5J / 4.184J/cal = 48.4 calories).
I guess that is the answer
Jennifer runs 5 miles east, then stops to take a break. after her break, she continues running 4 more miles east.
In this the total distance she covers is 9 miles and the total displacement is also the same as the distance that is 9 miles.
<h3>What is the difference between distance and displacement?</h3>
Displacement is the shortest distance between initial and final position, or we can say it is the straight-line distance between initial and final position.
Whereas distance is considered as the total path length covered from initial position till the final position. The Displacement of a body is always less than or equal to the distance.
Displacement can be zero in case the initial and final positions coincide, but distance can never be zero.
To know more about distance and displacement, visit:
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-2/5 = 11k - k
-2/5 = 10k
-2/5/10 = k
-2/5 * 10 = k
-2/50 = k
k = -1/25.
-1/25 - 2/5 = 11k is true.
