MadSci Network: Physics
Query:

Re: At what point(s) on a parabolic curve is a moving particle a rest?

Date: Tue May 18 23:50:45 1999
Posted By: Gerald Gels, Staff, Senior Health Physicist, Tetra Tech NUS Corp
Area of science: Physics
ID: 926085493.Ph
Message:

In the familiar rectilinear (X-Y) coordinate system, a particle moves 
along a parabolic path in two dimensions.  The component of velocity along 
the Y-axis will decrease and actually become zero at the peak of the 
parabola, before reversing direction and beginning to move in the opposite 
direction with increasing speed.  In this coordinate system, the X-
component of velocity will remain non-zero.  In fact, if we are talking 
about the parabolic trajectory of a particle under the influence of 
gravity, and if frictional forces are ignored, the component of velocity 
along the X-axis will remain constant.  Thus, if you consider velocity to 
be a vector quantity having both magnitude AND direction, the only way it 
could ever be zero would be when the X-component of velocity is zero.  
That is, when the particle is given an initial velocity directly upward 
(opposite the acceleration of gravity, in the Y-direction).  Then, the 
velocity would become zero momentarily when the particle reached its 
highest point.

In other coordinate systems, similar effects would be seen.  For instance, 
if one were to examine the parabolic trajectory in the polar coordinate 
system, the angular component would never become zero, but would approach 
zero at great distances from the center of the system.  And, the radial 
component of velocity would appear to be at rest at the point of closest 
approach to the focus of the parabola.

In fact, a particle could be constrained to move in a parabolic path and 
still have any imaginable velocity and acceleration components.  Usually 
in physics when we talk about particles moving in a parabolic path, we are 
intending to describe the path of a particle given an initial velocity in 
a gravitational field.  If that is the situation you are asking about, the 
velocity becomes zero only when both the X- and the Y- components are both 
zero.  That would only happen in the extreme case of a particle given an 
initial velocity directly upward (in the Y-direction).


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