Show that the speed of the object is constant

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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?
 

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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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