# Homework Help: Vector Proof Of Constant Speed Means Perpendicular Acceleration.

1. Jan 28, 2013

### Baumer8993

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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.

2. Jan 28, 2013

### clamtrox

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

3. Jan 28, 2013

### Staff: Mentor

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

4. Jan 28, 2013

### LCKurtz

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 $\vec V\cdot \vec V$.

5. Jan 28, 2013

### Baumer8993

How do you differentiate v dot v?

6. Jan 28, 2013

### ehild

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

ehild

7. Jan 28, 2013

### Baumer8993

Oh well duh that makes sense.

8. Jan 28, 2013

### LCKurtz

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