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motion; by a velocity distinguish a motion with variable and constant
velocity.
The most total classification of motion of particle is by its
acceleration. As be shown, in general case acceleration of particle is
determined by
=
aa n + a t . 2-37
Consider partial cases:
1. The normal acceleration of a particle equals zero, than a = ,
0
n
v 2 = 0. Certainly, if the particle moves v≠ , then ρ→∞. Only for a
0
ρ
line the radius of curvature approaches to infinity, consequently, the
particle moves along a straight line. For rectilinear motion the
velocity of the particle does not change direction, it means, that
normal acceleration of the particle represents the change of the
velocity by direction.
2. Obviously, if the normal acceleration of the particle does not
equal zero (a n ≠ 0), the particle moves on a curvilinear trajectory.
3. The tangential acceleration of a particle equals zero, than
a = 0. Thus a = dv t / dt = 0 and so v = const and v const= .
t
t
t
Consequently, in this case we have motion with constant
velocity. Take account of that ds v dt=⋅ and integrate this formula. We
t
obtained the equation of motion
s s= 0 + vt , 2-38
t
here s is an initial arc coordinate, that a value of arc coordinate is in
0
the moment of time t = 0.
This equation does not take account of the normal acceleration.
It means that the motion of particle along both curvilinear and
rectilinear path is described the same equation s s= 0 + vt. It proves
again that the tangential component of acceleration represents the
change of the magnitude of the velocity.
4. The tangential acceleration of particle does not equal a zero,
but it is permanent, that a = const ≠ 0.
t
Thus, we can write

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