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

[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.

 

[berkeman]

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?

 

[SammyS]

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

 

[ME_student]

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.