Show that the speed of the object is constant

[Dukefool]

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$\bullet$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?

 

[SammyS]

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$\bullet$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?

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

So, what if $\displaystyle \vec{v}\cdot\vec{a}=0\ ?$

Then $\displaystyle \vec{v}\cdot\frac{d\vec{v}}{dt}=0\ .$

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