# What does negative acceleration really mean?

1. Aug 25, 2011

### Genecks

I've read that negative acceleration can mean two things:

1) Something is slowing down
2) Something is speeding up in the opposite direction

Can it mean those two things at the same time?

So, if I'm driving a car at 30 mph, and then I slow down... how is it that the car is speeding up in the opposite direction? That doesn't seem right. I would agree that it is slowing down, though.

Because it would appear that the car is not be negatively displaced.

It seems like the real situation is distance traveled is changed. And acceleration denotes the direction of travel.

So, negative acceleration in the positive direction is deceleration, but negative acceleration in the opposite direction is basically increasing speed in the opposite direction? Right?

Last edited: Aug 25, 2011
2. Aug 25, 2011

### tiny-tim

Hi Bio-Hazard!

Negative acceleration Northwards means that your speed Northwards is decreasing.

If it was > 0, it's getting nearer 0.

If it was < 0. it's getting further from 0.

(And negative acceleration Northwards is always positive acceleration Southwards)

3. Aug 25, 2011

### olivermsun

To have a +/- sign attached to your speed you need to define which way is "forward." Then, forward motion is positive and the other way is negative. Similarly, acceleration in the forward direction is positive and the other way is negative.

If northbound on the freeway is positive, then southbound cars speeding up have "negative" acceleration -- they're speeding up in the negative direction.

Obviously, accelerating with your current direction of travel will cause you to "speed up," and accelerating against your current direction of travel will cause you to "slow down."

4. Aug 25, 2011

### Hootenanny

Staff Emeritus
In addition to what Tim and Oliver have said, I'd just like to add a couple of comments.

In my honest opinion, Deceleration is a horrendous term and one which causes unnecessary confusion. It is best to just confine yourself to acceleration. Indeed, beyond high school physics or mechanics, I would be surprised if you hear the term “deceleration” used by a teacher, mathematician, physicist, engineer etc. In any case, the term deceleration means the “opposite” of acceleration and is therefore somewhat redundant.

When thinking about positive and negative acceleration, it often simplifies matters if you think of velocity, rather than speed. Then, a positive acceleration means than the velocity is increasing and a negative acceleration means that the velocity is decreasing.

5. Aug 25, 2011

### robphy

Since acceleration is a vector,
you need a dot-product with another vector [which must be specified]
to get a [e.g., "negative"] number.

For simplicity, let us assume that all accelerations and velocities are along the x-axis.

So, here is one vector: x-hat (the unit vector in the x-direction).
So, a_x is negative, which means that the x-component of the velocity is decreasing.
While v_x is positive, then v_x decreases means the speed abs(v_x) will decrease toward zero.
While v_x is negative, then v_x decreases means the speed abs(v_x) will increase away zero.

Now, here is another vector: the velocity vector (with no specification of where it points, along x-hat or opposite x-hat or variable).
While a-dot-v is positive (that is, a points in the same direction as v),
the speed increases (since v's magnitude increases).
While a-dot-v is negative (that is, a points in the opposite direction to v),
the speed decreases (since v's magnitude decreases)... sometimes called "deceleration".
[Note that (d/dt(v-dot-v)=2v-dot-(dv/dt)=2v-dot-a.]

[One needs to distinguish
the "x-component of velocity" (v-dot-xhat)
from the "speed" (sqrt(v-dot-v))

6. Aug 25, 2011

### mender

Motion is relative; a change in motion is also relative.

7. Aug 25, 2011

### K^2

Change in motion is absolute.

Edit: Well, I suppose it depends on what you mean. Acceleration is absolute, while the partial derivative of velocity with respect to time will depend on frame of reference.

8. Aug 26, 2011

### Lsos

Since motion is relative, a car decelerating or accelerating is the exact same thing. It is simply the change in velocity. If you're standing on the ground and looking at the car slowing down, it might not make sense to say he is "accelerating in the opposite direction".

But take away your frames of reference (the ground), and imagine you are flying in space next to another spacehip. You might be both moving at 1000 mph or 1000000000mph relative to the earth, but either way to each other you both look like you're standing still. Then if the other spaceship "slows down" relative tot the earth...to you it indeed looks like he is accelerating in the other direction.

So you see it is the same thing, just looking at it from different perspectives. No instrument will tell you whether you are slowing down or speeding up unless you give it a frame of reference. It will simply tell you how fast you are accelerating, and in which direction.

9. Aug 26, 2011

### mender

Yeah, what you said is what I meant; thanks for phrasing it properly.

10. Aug 26, 2011

### MrREC

I don't know physics at all but....... If I were in a car moving north then that would be "positive acceleration". If at some point (a) I shot a gun from the car due south then would not the bullet also be under positive acceleration in relation to point (a)?

Would the bullet and the car both be in a state of "negative acceleration" in relationship to each other but both be in a state of "positive acceleration" from point(a)?

If I understand what everyone is saying correctly "acceleration" is perspective momentum. If I'm in the car going forward that's positive. If I'm the bullet going forward that's positive also. Negative would be the opposing relationship between the two?

So as a matter of perspective both can be positive, negative or either?

11. Aug 26, 2011

### WannabeNewton

You define the positive and negative directions relative to a frame of reference and observe the car and bullet from that frame.

12. Aug 26, 2011

### MrREC

If I am standing at point (a) and the car and bullet are receding from me in opposite directions I assume then that my acceleration would be 0.

What then would be state of the car and the bullet. Would they both then be positive because they are moving away from me.

If I were just facing the car would it be positive and the bullet negative, or would they remain in the same state?

13. Aug 27, 2011

### Hootenanny

Staff Emeritus
You're acceleration [and speed] in your frame of reference would be zero. From the frame (read point of view) of the car and bullet, your acceleration and speed would be non-zero.
This would depend on how you define your frame of reference. Think of a frame of reference as a coordinate axis (e.g. an x-axis and a y-axis). You are free to draw your co-ordinate axes as you like. So, if you draw your co-ordinate axes with the x-axis pointing along the line of travel of the bullet, then the bullet's velocity would be positive. If the bullet's velocity was decreasing (increasing) its acceleration in your frame of reference would be negative (positive). On the other hand, the car would be travelling along the negative x-axis and therefore would have negative velocity according to your frame of reference.

Obviously things would be different if viewed from the frame of reference of the car or bullet.

Does that help?

14. Aug 27, 2011

### MrREC

.

Does that help?[/QUOTE]

Yes.....Thanks.

15. Aug 27, 2011

### sophiecentaur

One situation where you can easily see the two as equivalent to each other is with a spacecraft. Start with it batting along at a high speed in the forward direction. (As observed from the Earth, say).
It then starts to fire its retro rockets. First it will slow down - then it will be seen to accelerate in the 'backwards' direction. The same force has been applied all the time from the rockets and that force makes it do both 1. and 2. in your original question.
If someone were to be alongside the rocket, doing the same original speed, as soon as the retro rockets were fired, it would just see our rocket accelerating backwards, from the start. (We've all seen the free fall parachute films when everyone appears to be shooting up in the air when they pull their cords and the camera is still in free fall - same thing).

So 1. and 2. must be equivalent and there's no contradiction.
So they must be equivalent to each other.

16. Aug 27, 2011

### stallionx

It simply is dV/dt = a where V, a are vectors

(Vf-Vi)/dt<0

Vf<Vi

no matter the directions the length, hence the magnitudes of V decrease.

Simply put : decrease in magnitude of the velocity magnitude which is Speed.