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Zay d

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In summary, the conversation discusses the relationship between velocity and acceleration in uniform circular motion. The equation for circular motion is r(t)=cos(t)i+sin(t)j, and by differentiating it twice, we can find the speed and acceleration vectors. It is noted that in this case, the velocity and acceleration vectors are perpendicular to each other, which can be visualized by drawing a circle and observing their positions. However, this is not always the case in real-life situations.

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Zay d

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RyanH42

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The circular motion equation is

Perpandicular means dot product will be zero.So you need to find v.a=? Find it and then share the answer here so I can be sure you find true answer.

- #3

insightful

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1. Draw a circle with vector

2. Picture

3. Consider

4. A very short time later (dt),

5. To get d

6. Construct a small vector with the tail at the tip of

7. It should be clear that d

8. Since d

Hope this helps.

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sophiecentaur

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Velocity refers to the rate of change of an object's position with respect to time, while acceleration refers to the rate of change of an object's velocity with respect to time. In other words, velocity measures how fast an object is moving, while acceleration measures how quickly its speed is changing.

Yes, an object can have a velocity perpendicular to its acceleration. This occurs when the object is moving in a circular motion, such as a car going around a roundabout. The car's velocity is constantly changing direction, while its acceleration is directed towards the center of the circle.

Velocity perpendicular to acceleration can be calculated using vector mathematics. The perpendicular component of velocity can be found by taking the dot product of the object's velocity vector and the unit vector perpendicular to its acceleration vector.

The significance of velocity perpendicular to acceleration lies in its relationship to circular motion. In circular motion, the acceleration is always directed towards the center of the circle, while the velocity is constantly changing direction. This allows objects to maintain a constant speed while still changing direction.

The velocity perpendicular to acceleration determines the curvature of an object's trajectory. The greater the perpendicular velocity, the sharper the curvature of the trajectory will be. This is why objects moving in circular motion have a constantly changing direction, as their perpendicular velocity is constantly changing.

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