# Determining the sign (direction) of velocity

#### borophyll

Hi all,

Regarding the kinematic equation for rectilinear motion (acceleration constant):

$image=http://latex.codecogs.com/png.latex?v^2+=+v_0^2+++2a(x+-+x_0)&hash=ada4fa1cc2c0fff499af1ce3c9d7debd$

how do you determine the sign of the velocity? v^2 is always positive, but how do you determine whether v is positive or negative? For example, consider the input variables to be:

$image=http://latex.codecogs.com/png.latex?v_0+=+20,+a+=+-10,+x_0+=+0,+x+=+15&hash=e045d464322947a62a790b9a30af153a$

The velocity is negative, but it seems that this equation alone gives no indication of the sign. In fact, at first sight, you might just assume that the velocity is positive, because the displacement has increased by +15. However, the velocity is actually negative, because the object first travels 20m, then changes direction and moves back another 5m to give 15m as the final displacement. The only reason I know this is because I created the example myself.

Anyone care to shed some light on this?

#### borophyll

Hmm, actually, I may need to think about this more, I just realized it could be positive OR negative, depending on at what time you observe the object at that position.

So, I guess you have to examine the sign of the initial velocity and acceleration. If they are different, both answers are reasonable. If they are the same, then use that sign for the velocity in the final answer. Does that sound correct?

Last edited:

#### Unknown008

PHF Hall of Honor
Yes, that's right

borophyll