Average Velocity and Instantaneous Velocity
If a particle moves through a displacement t:.r in a time interval , then its average velocity v is,
The direction of the instantaneous velocity V of a particle is always tangent to the particle’s path at the particle’s position,
The result is the same in three dimensions: v is always tangent to the particle’s path. To write in unit vector form, we substitute for r,
This equation can be simplified somewhat by writing it as
where the scalar components of are
For example, scalar component of v along the axis. Thus, we can find the scalar components of v by differentiating the scalar components of F.
However, when a velocity vector is drawn as in, it does not extend from one point to another. Rather it shows the instantaneous direction of travel of a particle located at the tail, and its length (representing the velocity magnitude) can be drawn to any scale.
CHECKPOINT 2: The figure shows a circular path taken by a particle. If the instantaneous velocity of the particle, through which quadrant is the particle moving when it is traveling (a) clockwise and (b) counterclockwise around the’circle? For both cases, draw V on the figure.