# Is acceleration vector or scalar?

## Homework Statement

I am a teacher currently teaching very introductory physics. I just came across a test question asking the students to choose whether acceleration is vector or scalar.

## The Attempt at a Solution

I have always thought that acceleration can be either vector or scalar. For example, we call 4 m/s a "speed", and 4 m/s west a "velocity". Similarly, 10 m/s2 is scalar while 10 m/s2 west is a vector, but they are both just called "acceleration".

Am I wrong? Thank you in advance!

## Answers and Replies

haruspex
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Acceleration always has a direction so should always be taken to be a vector. If you only mean the magnitude then that's the magnitude of the acceleration.

vela
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Sometimes you have to infer the direction from the context of the problem rather than it being stated explicitly. But there should always be a direction associated with an acceleration.

pitbull
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Acceleration is, like velocity, a vector.

The term speed is used when it is not important to specify the direction or the direction is unknown.... But that doesn't mean the object's momentum is directionless. Both velocity and acceleration are vector components as they are always associated with force. Rather than seeing this through physics we should understand the verbal comfort associated with it.

Delphi51
Homework Helper
Hi Jumbogala - I was also a high school physics teacher and I saw what you describe in textbook lists of scalar and vector quantities. There are separate terms for speed/velocity (though the word velocity is often used for both), but acceleration was listed twice because there is no separate term for scalar acceleration. It is common to not bother with direction in one dimensional problems such as an object falling straight down.

Mark44
Mentor
Hi Jumbogala - I was also a high school physics teacher and I saw what you describe in textbook lists of scalar and vector quantities. There are separate terms for speed/velocity (though the word velocity is often used for both), but acceleration was listed twice because there is no separate term for scalar acceleration. It is common to not bother with direction in one dimensional problems such as an object falling straight down.
On the other hand, even in one-directional problems with a falling object you can have forces acting in opposite directions; gravitational acting downward and drag acting upward. These forces are associated with accelerations with opposite signs. In problems such as these it's important to treat acceleration as a vector quantity.

Hi Jumbogala - I was also a high school physics teacher and I saw what you describe in textbook lists of scalar and vector quantities. There are separate terms for speed/velocity (though the word velocity is often used for both), but acceleration was listed twice because there is no separate term for scalar acceleration. It is common to not bother with direction in one dimensional problems such as an object falling straight down.

Yes, this is exactly what I'm talking about! I understand that there are situations where acceleration has to be treated like a vector quantity (such as in Mark44's post). So it would actually be incorrect to say that acceleration can ever be scalar?

vela
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Yes, it's incorrect.