Vector Proof Of Constant Speed Means Perpendicular Acceleration.

[Baumer8993]

Homework Statement

Prove that when speed is constant that V(T), and A(T) are perpendicular.

Homework Equations

I know this involves the dot product to show that the dot product of the vectors is zero.

The Attempt at a Solution

In my head I thought that since the speed is constant that there must be no acceleration. When I dot the zero acceleration vector to the velocity vector it is zero, but I am thinking that there is no way this can be right.

 

[clamtrox]

What is "speed"? I'm guessing V and A are vectors

 

[Mark44]

Homework Statement

Prove that when speed is constant that V(T), and A(T) are perpendicular.

Homework Equations

I know this involves the dot product to show that the dot product of the vectors is zero.

The Attempt at a Solution

In my head I thought that since the speed is constant that there must be no acceleration. When I dot the zero acceleration vector to the velocity vector it is zero, but I am thinking that there is no way this can be right.

How does speed relate to velocity? Your book should give a definition for speed.

 

[LCKurtz]

Homework Statement

Prove that when speed is constant that V(T), and A(T) are perpendicular.

Homework Equations

I know this involves the dot product to show that the dot product of the vectors is zero.

The Attempt at a Solution

In my head I thought that since the speed is constant that there must be no acceleration. When I dot the zero acceleration vector to the velocity vector it is zero, but I am thinking that there is no way this can be right.

That isn't true. For example, in uniform circular motion the speed is constant but the acceleration is nonzero towards the center. Think about differentiating $\vec V\cdot \vec V$.

 

[Baumer8993]

How do you differentiate v dot v?

 

[ehild]

It is a product. How do you differentiate a product?

ehild

 

[Baumer8993]

Oh well duh that makes sense.

 

[LCKurtz]

Of course, you first have to prove that the product rule works for dot products of vectors.