Ghaleb -
In a nutshell, if an objects acceleration is positive this means
that its velocity is changing in such a way that it is becoming more
positive. Similarly, if an objects acceleration is negative this means
that its velocity is changing in such a way that it is becoming less
positive.
Lets think about this a bit more:
The acceleration of an object is the rate of change of its
velocity. In order to define this properly you need to know which
direction is being called positive. For example, suppose you are
driving north at 60 mph along a highway that runs north-south. If you
pick north to be positive, your velocity is +60 mph. If you pick south
to be positive, your velocity is -60 mph. This may seem like a
technicality, but its important to understand if you are worrying about
the sign of acceleration.
Suppose you have picked north to be positive, and your velocity is
initially +60 mph. If you step on the gas to pass a truck, your
velocity is becoming more positive (i.e. it may go up to +80 mph) so
your acceleration is positive. If you step on the brakes to slow down,
your velocity is becoming less positive (i.e. it may go down to +40
mph) so your acceleration is negative.
Now suppose you have picked north to be positive, and your velocity
is initially -60 mph (in other words, you are driving south). If you
step on the gas to pass a truck, your velocity is becoming more
negative (i.e. it may go to -80 mph) so your acceleration is negative.
If you step on the brakes to slow down, your velocity is becoming less
negative (i.e. it may go to -40 mph) so your acceleration is positive.
So, the sign of the acceleration depends on the sign of the change
of the velocity. A good way to remember all this for the simple
1-dimensional case of a car on the road is the following: If you are
speeding up, the direction of your acceleration and your velocity are
the same. If you are slowing down, the direction of your acceleration
and your velocity are the opposite.
In mathematical terms we say that both velocity and
acceleration are "vector" quantities, which means that they have a
direction as well as a magnitude. In the simple 1-dimensional case of a
car on a road we can specify the direction by specifying the sign
(recall the difference between the car having a velocity of +60 mph and
-60 mph as discussed above). In general, things can be even more
interesting. If you are driving a car around a circular track at a
constant speed, for example, your velocity is constantly changing since
the direction of your velocity is changing as you turn. The result is
that in this situation your acceleration points toward the center of
the circle the whole time.
Mats
(published on 10/22/2007)
