Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
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05. A particle moves so that its position vector is given by
r cos t
i
sin t
j,
is
a
cons tan t
show
that
i) velocity v
is perpendicular to
r
ii) acceleration
to the distance from the origin.
a is directed towards the origin and has magnitude proportional
iii) r x v is a cons tan t vector.
Suggested answer:
i)
r cos t
i sin t
j
d r
dt
sin t
i cos t
j v
Now
v . r 0
v r
ii)
a
d
2
r
dt
2
2
cos t
i sin t
j
a
2
r
| a | 2
| r |
iii)
r x v
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