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

Engineering Mathematics - II - Vector Calculus - 2007
Note 1:
d r
dt
represents
the
velocity
v
(rate
of
change
of
position
with
which
the
ter min al po int
of
r
describes the
curve )
Note 2:
d r
dt
is
along
the
direction
of
the
tan gent
to
the
space
curve
at
P (x, y, z)
Note 3:
The
unit
tan gent
vector
to
the
space
curve
is
denoted by
t
and
is given by
t
d r
dt
d r
| |
dt
Note 4:
d v
dt
d
2
r
is called the acceleration a
dt
2
of
the
curve
at time
t.
Unit Normal to a Space Curve
Let A be a fixed point on the curve and s be the length of the arc AP where
P(x,y,z) is a point on the space curve.
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