# Scalar vs Vector

1. Jul 16, 2011

### Torshi

I came across a problem that asked if some things were scalar or a vector.

Is acceleration a vector? I thought it just gives you magnitude and not direction at all.

For example when velocity and acceleration are put together, velocity gives you the direction and the acceleration gives tells you if your slowing down or speeding up?

I'm not understanding these terms.

Also, mass is suppose to be scalar right? My prof at first said it as a vector then the next day he writes it's scalar. I understand vector means direction and magnitude

2. Jul 16, 2011

### mathman

Acceleration is a vector. Changing direction is considered acceleration, like driving around a curve at constant speed.

Mass is a scalar.

3. Jul 16, 2011

### Torshi

So like if your acceleration is slowing down, you'll eventually go the other direction? That's how it was explained to me.

4. Jul 16, 2011

### Pengwuino

That's a poor choice of wording. "Speeding up" and "slowing down" are terms that only really make sense for speed.

Imagine yourself with a rocket strapped onto a car. Define your coordinate system so that going to the right is positive and going to the left is negative.

So start at rest, point your rocket to the right. When you light the rocket, the acceleration is pointing to the right and your car starts speeding up and it begins to have a positive velocity (in other words, it's moving to the right). That's simple enough.

Now, while your car is rocketing off to the right (in other words, with a positive velocity), you decide to switch the direction of your rocket all of a sudden and point it to the left. Now your acceleration is pointing to the left and is now negative! Your velocity is still positive because the rocket needs time to slow the car down and eventually start moving in the other direction. So your velocity is positive, the acceleration is negative; the positive/negative is showing the direction. They're both vectors.

5. Jul 16, 2011

### gsal

Acceleration, a, is a vector

Mass, m, is a scalar

Weight is again a vector, since it is F=ma

Now, let's say that you have an initial (positive) velocity going up and constant negative acceleration going down...eventually, the acceleration will slow down the object to zero velocity and then start increasing the velocity in the negative direction....

....this is exactly what happens when you throw a ball straight up in the air...get it?

6. Jul 16, 2011

### I like Serena

This reminds me of a discussion whether speed is a vector or not.

Apparently velocity is a vector, while speed is its magnitude.

It seems that the word acceleration is ambiguous and depends on the context.

7. Jul 17, 2011

### mathman

There is no ambiguity - acceleration is a vector. You may accelerate along the direction you are going or change direction (or both together).

8. Jul 17, 2011

### I like Serena

I agree that acceleration should always be a vector, physically speaking.

But I got this from wikipedia: "In common speech, the term acceleration is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration."

In my book that means it's ambiguous.
Apparently physicists use the same word to mean something different from what it means to the common man.
I believe that this ambiguity is exactly what prompted the OP to start this thread.

The nice thing about the word velocity is that it is not used in common speech, while the word speed is.
That gave physicists the opportunity to define velocity to be a vector, which they did.

Last edited: Jul 17, 2011
9. Jul 17, 2011

### tiny-tim

Hi Torshi!
mass is definitely a scalar
Yes, in maths and physics acceleration means a vector, but it ordinary English it often means dv/dt, which is a scalar.

dv/dt (rate of change of speed) is the rate of change of what is shown on your speedometer.

For example, if you drive at variable speed v, then your tangential component (ie the forwards component) of your acceleration is dv/dt, but your sideways component (ie the centripetal acceleration) is v2/r , where r is the (instantaneous) radius of curvature …

and your total (vector) acceleration is the (vector) sum of those two perpendicular components.

We can write F = ma where both F and a are the components in a particular direction,

or we can write F = ma where both F and a are the complete (vector) force and acceleration.

10. Jul 17, 2011

### Pengwuino

I've always seen it as ${{d \vec v }\over{dt}}$ so the ambiguity doesn't exist.