Meaning of Sign of the Variables of Motion for One Dimensional Motion
Frame
of Reference:
Before
we can talk about the meaning of the sign of a variable we must first specify
the frame of reference from which we will view the motion of some object. The
following choices are up to you to specify and your choice will determine the
outcome of the meaning of the sign of a variable. We will assume the body is
moving horizontally.
Spacial Frame:
We also need to stipulate were the origin is located and which direction relative to the origin – to the right or left – will be taken as
the positive direction. We will assume the normal convention that the positive
direction is to the right of the origin.
Time Frame:
We also need to specify when we will start the clock – the origin of time.
Time Variable t:
t
>
0
– some moment after the instant we start the clock.
t
<
0
– some moment before the instant we start the clock.
Position Variable x:
x
> 0 –
the
body is to the right of the chosen origin.
x
< 0 –
the
body is to the left of the chosen origin.
- By shifting the origin one could make the value of the position of a body either positive or negative.
Velocity Variable v:
v
> 0 –
the
body is moving to the right. The body could be either to the right or left of
the origin.
v
< 0
–
the body is moving to the left. The body could be either to the right or left
of the origin.
Acceleration Variable a:
a
> 0
– the body is increasing its speed in the positive
x-direction.
This is not dependent upon whither the body’s velocity
v
is
to the right or left.
a
< 0
– the body is increasing its speed in the negative
x-direction.
This is not dependent upon whither the bodies velocity
v
is
to the right or left.
- Changing the location of the origin will have no effect on the sign or value of the body’s acceleration. What would change the sign of the body’s acceleration is our choice of which direction (to the right or left) is taken to be the positive direction.
- An object is commonly said to be accelerating if both a and v are in the same direction – either ( v > 0 and a > 0 – the body is accelerating in the positively chosen direction) or ( v < 0 and a < 0 - the body is accelerating in the negatively chosen direction). An object could be accelerating even if its value of acceleration is negative provided the object is also moving in the negative direction.
- An object is commonly said to be decelerating if a and v are in opposite directions – either ( v > 0 and a < 0) or ( v < 0 and a > 0) .
