Average Velocity and Instantaneous Velocity

Average Velocity and Instantaneous Velocity

If a particle moves through a displacement t:.r in a time interval , then its average velocity v is,

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 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,

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This equation can be simplified somewhat by writing it as

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The displacement !:lr of a particle during a time interval !:lr, from position 1 with position vector rl at time II to position 2 with position vector r; at time 12, The tangent to the particle'Spath at position I is shown.
The displacement  of a particle
during a time interval from
position 1 with position vector  at
time  to position 2 with position vector
at time 12, The tangent to the
particle path at position I is shown.

where the scalar components of are

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The velocity Vof a particle, along with the scalar components of V.
The velocity V of a particle,
along with the scalar components of V.

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.

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