Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
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d<br />
find i)<br />
dt<br />
Engineering Mathematics - II - <strong>Vector</strong> Calculus - 2007<br />
<br />
<br />
d <br />
d <br />
f , ii) f g iii) f x g <br />
<br />
<br />
dt<br />
<br />
dt<br />
<br />
Suggested answer:<br />
<br />
i) f e<br />
t<br />
i e<br />
3t<br />
j<br />
<br />
2te<br />
2t<br />
k<br />
d<br />
dt<br />
<br />
f e<br />
t<br />
<br />
<br />
<br />
i 3e<br />
3t<br />
j <br />
2<br />
<br />
<br />
2te<br />
2t<br />
<br />
<br />
e<br />
2t<br />
<br />
k<br />
<br />
ii)<br />
d<br />
dt<br />
<br />
<br />
f g (e<br />
t<br />
<br />
<br />
<br />
sin t) i ( e<br />
t<br />
<br />
cos t) j<br />
(<br />
<br />
2 1) k<br />
iii)<br />
<br />
f x g <br />
<br />
i j<br />
e<br />
t<br />
e<br />
t<br />
cos t sin t<br />
<br />
k<br />
2t<br />
t<br />
<br />
i( te<br />
t<br />
<br />
2t sin t)<br />
<br />
j(te<br />
t<br />
<br />
e<br />
t<br />
cos t) k(e<br />
t<br />
sin t e<br />
t<br />
)<br />
<br />
d <br />
( f x g) i te<br />
t<br />
e<br />
t<br />
2t cos t 2 sin t<br />
dt<br />
<br />
<br />
j e<br />
t<br />
te<br />
t<br />
e<br />
t cos t e<br />
t<br />
sin t<br />
<br />
<br />
k e<br />
t<br />
cos t e<br />
t<br />
sin t e<br />
t cos t e<br />
t<br />
sin t .<br />
<br />
<br />
<br />
03. A particle moves along the curve whose parametric coordinates are x = e -t ,<br />
y = 2 cos 3t, z = 2 sin 3t. Here t is time i) Determine its velocity <strong>and</strong><br />
acceleration at time t ii) find the magnitude of velocity <strong>and</strong> acceleration at t =<br />
0.<br />
Suggested answer:<br />
Page 38 of 72
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