# Q & A: Acceleration Sign

Q:
When the accelaration will be negative, zero or positive?
- Ghaleb
MONTREAL-NORD
A:
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.

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)