Velocity vector's change of direction

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SUMMARY

The discussion focuses on the behavior of velocity and acceleration vectors when an object's direction changes without a change in speed. It establishes that while the magnitude of the velocity vector remains constant, its direction can change, leading to a perpendicular relationship between the velocity and acceleration vectors. The key formulas presented are v = r / time for velocity and a = d v / dt for acceleration, emphasizing that these are vector quantities and that the direction of acceleration aligns with the change in velocity.

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boris16
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hi

If an object changes it's direction but not speed, then velocity vector will only change its direction but not magnitude.

* ... delta

*r... displacement vector

Formula for velocity change is *v = *r / *time

This formula doesn't tell us anything about the direction of *v, it tells us
only about its magnitude ?

Same could be said for acceleration vector a. Formula will only tell you acceleration vector's magnitude, but not it's direction ( well we do know the direction is same as *v, but since we don't know the direction of *v it's of little use ) ?

bye
 
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The correct "formulas" are

\vec v = \frac {d \vec r}{dt}

\vec a = \frac {d \vec v}{dt}

These are vector quantities. If the direction of the velocity changes without changing the speed, the velocity and acceleration are perpendicular to each other.
 

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