MadSci Network: Physics |
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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