
11Kinematics
© 2010 Taylor & Francis Group, LLC
In terms of
rt xteyte zte() ()
ˆ
()
ˆ
()
ˆ
=++
123
, the acceleration
is given by
a
r
t
x
t
e
y
t
e
z
t
e==
d
d
d
d
d
d
d
d
2
2
2
2
1
2
2
2
2
2
ˆˆˆ
,
and its magnitude is
aa aa xt yt zt== ⋅=
(/)(/)(/)dd dd dd
222222
2
.
Whenever the words “velocity” and “acceleration” are used hereafter, they shall be taken to mean
the instantaneous values unless otherwise specied.
It should be noted that
/
is not at all the same thing as the derivative dr/dt of the magni-
tude of r with respect to t. Consider, for example, a particle moving with constant speed in a circle
the center of which is at the origin. As r is constant, dr/dt is ...