# Kinda silly, but what's the sign of v?

• 0kelvin
In summary: If v is positive then the block is moving to the right and if v is negative then the block is moving to the left.
0kelvin
I have a block with a certain mass attached to a spring. I pull it and then release. Spring pulls block back. When spring is back to its relaxed position, is the velocity of the block positive or negative? Exercise does provide k, mass and x, but that's not where the error is comming from.

According to the law of conservation of energy I have:

$$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$$

I imediately though that since the usual orientation is x is positive to the right and block is moving to the left, velocity should be negative. But there is an example like this in the book and velocity is positive. How so? Absolute value is right, but the sign is wrong.

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0kelvin said:
I have a block with a certain mass attached to a spring. I pull it and then release. Spring pulls block back. When spring is back to its relaxed position, is the velocity of the block positive or negative? Exercise does provide k, mass and x, but that's not where the error is comming from.

According to the law of conservation of energy I have:

$$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$$

I imediately though that since the usual orientation is x is positive to the right and block is moving to the left, velocity should be negative. But there is an example like this in the book and velocity is positive. How so? Absolute value is right, but the sign is wrong.

Just define your axes and relate all quantities to them. Can you post a diagram so we can help clarify your question?

Whether v is positive or negative, what is the sign of v2 ?

This is how I think about it. Since we have T=1/2mv^2, T is nothing more than energy. Is energy a scalar or vector? It's a scalar, has no direction. So I believe energy doesn't have a direction so the negative sign will disappear. I used T instead of V since we use T a lot in dynamics.

## What is the sign of v?

The sign of v refers to the direction or orientation of the velocity vector. It can be positive or negative, indicating whether the object is moving in the positive or negative direction.

## How is the sign of v determined?

The sign of v is determined by the direction in which the object is moving. If the object is moving in the positive direction, the sign of v is positive. If the object is moving in the negative direction, the sign of v is negative.

## What does a positive sign of v indicate?

A positive sign of v indicates that the object is moving in the positive direction. This means that the object is moving away from the point of reference in a straight line.

## What does a negative sign of v indicate?

A negative sign of v indicates that the object is moving in the negative direction. This means that the object is moving towards the point of reference in a straight line.

## Can the sign of v change?

Yes, the sign of v can change if the direction of motion changes. For example, if an object is initially moving in the positive direction and then changes to the negative direction, the sign of v will also change accordingly.

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