# Prove that v(t) is any vector that depends on time

#### Oblio

i know i shoul get the magnitude of v.. but how from 0?

#### learningphysics

Homework Helper
i know i shoul get the magnitude of v.. but how from 0?
You're integrating both sides of:

2v.a = 0

what's the integral of the 0?

#### Oblio

the scalar of v..

#### learningphysics

Homework Helper
the scalar of v..
yeah, it will turn out to be |v|^2... but when we integrate 0, we get C...

ie: integral of 0, is just a constant, so you can just call the right side C.

ie:

$$\vec{v}\cdot\vec{v} = C$$

#### Oblio

I need to work it to v^2?

Was the multiplying by two only by the knowledge of doing the first part?

#### learningphysics

Homework Helper
I need to work it to v^2?

Was the multiplying by two only by the knowledge of doing the first part?
yeah sort of... for the second part you somehow need to figure out that $$\frac{d(\vec{v}\cdot\vec{v})}{dt} = 2\vec{\frac{dv}{dt}}\cdot\vec{v}$$

we already proved this in the first part.

so yes, v.v = |v|^2

|v|^2 = C, so |v|=sqrt(C), which is a constant.

#### Oblio

Alright, I wasn't sure if multiplying by two was also a reasonable 'step' without the preknowledge.

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