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Show that the speed of the object is constant

  • Thread starter Dukefool
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Homework Statement


Suppose an object moves in such a way that its acceleration vector is always perpendicular to its velocity vector. Show that speed of the object is constant.


Homework Equations


For two vectors to be perpendicular: A[itex]\bullet[/itex]B=0
Speed of the object = ||Velocity Vector||


The Attempt at a Solution


I have no idea how to approach this question. How can the speed of the object affect whether or not the acceleration vector is perpendicular to the velocity vector?
 

Answers and Replies

  • #2
SammyS
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Homework Statement


Suppose an object moves in such a way that its acceleration vector is always perpendicular to its velocity vector. Show that speed of the object is constant.

Homework Equations


For two vectors to be perpendicular: A[itex]\bullet[/itex]B=0
Speed of the object = ||Velocity Vector||

The Attempt at a Solution


I have no idea how to approach this question. How can the speed of the object affect whether or not the acceleration vector is perpendicular to the velocity vector?
[itex]\displaystyle \vec{a}=\frac{d\vec{v}}{dt}[/itex]

So, what if [itex]\displaystyle \vec{v}\cdot\vec{a}=0\ ?[/itex]

Then [itex]\displaystyle \vec{v}\cdot\frac{d\vec{v}}{dt}=0\ .[/itex]

Can you write the left-hand side of that last expression in a different way?
 

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