Whether constant acceleration and zero acceleration are the same

[Mathivanan]

In the equation v=u+at, u=5 m/sec and a=0, then v=5 m/sec. That means the body is moving with a constant velocity of 5 m/sec. In a velocity-time graph, the equation produces a straight horizontal line. Some texts say the body is moving with zero acceleration and others say it is moving with constant acceleration. Which is correct?

 

[scottdave]

If the constant is equal to zero, then they both can be right. I usually see constant acceleration to mean a nonzero constant, though.

 

[Dale]

Some texts say the body is moving with zero acceleration and others say it is moving with constant acceleration.

Isnt zero a constant? What is the confusion here?

 

[Ibix]

We do tend to make a distinction between "not doing something" and "doing something" in natural language. But maths regards it as a distinction without a difference. So, as others have noted, zero is just a constant like any other.

 

[Mathivanan]

Isnt zero a constant? What is the confusion here?

The confusion is: what is the need for qualifying acceleration as constant; it is positive or negative or zero, in all these cases it's a constant.

 

[Mathivanan]

We do tend to make a distinction between "not doing something" and "doing something" in natural language. But maths regards it as a distinction without a difference. So, as others have noted, zero is just a constant like any other.

Inaction and action are both actions, right!

 

[scottdave]

There are formulas for constant acceleration. These formulas work just fine when acceleration is a constant zero - they can be written in simpler terms, because a=0.
Everything changes when you have a non-constant (changing) acceleration, though.

 

[vanhees71]

Constant acceleration implies
$$\ddot{\vec{x}}=\vec{a}=\text{const}.$$
Integrating twice with respect to time, gives immediately
$$\vec{x}(t)=\frac{\vec{a}}{2} t^2 + \vec{v}_0 t + \vec{x}_0,$$
where $\vec{v}_0$ is the velocity of the body at time $t=0$ and $\vec{x}_0$ is its position at time $t=0$.

Nothing in the above calculation forbids me to apply it to the special case $\vec{a}=0$, where of course, you get uniform motion (i.e., motion with constant velocity), as it must be from Newton's 1st law:
$$\vec{x}(t)=\vec{v}_0 t + \vec{x}_0.$$

 

[Dale]

The confusion is: what is the need for qualifying acceleration as constant; it is positive or negative or zero, in all these cases it's a constant.

Acceleration need not be constant. A simple example is a spring and simple harmonic motion. The acceleration varies over time, it is not constant.

The "suvat" equations do not apply for such motion.

 

[Dadface]

The word "zero" can be used more descriptively and more economically than the word "constant" because it can be more specific. Here's an example comparing the use of the two words in describing the motion of an object during a certain time interval:
1. During that time interval the acceleration of the object was zero.
2. During that time interval the acceleration of the object was constant.
For sentence two to be as specific as sentence one it would need to be added to to give the value of the acceleration.

 

[Mathivanan]

What I thought is: a body is said to have zero acceleration when it is either at rest or comes to rest if it's moving; it is because acceleration due to gravity. In the equation v=u+at, when a=0, the body moves with a constant velocity. Can we say that the body is moving with zero acceleration? If it is how a body can move with constant velocity without acceleration. It should have a positive acceleration to move with constant velocity. Hence 'a' cannot be zero. Therefore, there is something wrong with my understanding. In the equation, 'a' is not simply acceleration but rather a change in acceleration or Δa. As a body cannot be moved without acceleration, it has an initial acceleration. When there is no change in the initial acceleration, that is Δa=0, the body moves with constant velocity. It seems the equation is v=u+Δa*t.

 

[ZapperZ]

The confusion is: what is the need for qualifying acceleration as constant; it is positive or negative or zero, in all these cases it's a constant.

Zero acceleration is a SPECIAL CASE of constant acceleration.

Zero acceleration is a member of constant acceleration set. However, a constant acceleration does NOT mean the acceleration is zero.,

There are numerous other examples of this. A uniform, zero potential is a special case of a constant potential. However, a constant potential does not imply a potential value of zero.

Zz.

 

[boringelectron]

Constant acceleration means that the velocity with which an object is moving with is constantly changing with time
This gives us a horizontal line in acceleration/time graph.

If the acceleration is zero means that the object is moving at a constant velocity which is a straight line on a velocity/time graph.

Constant acceleration can not be zero

 

[Ibix]

Constant acceleration can not be zero

No. Constant acceleration means $da/dt=0$. That is satisfied by any $a$, zero or non-zero, that does not vary with time.

 

[Ibix]

What I thought is: a body is said to have zero acceleration when it is either at rest or comes to rest if it's moving; it is because acceleration due to gravity.

This isn't right. A body moving at constant velocity has zero acceleration, whether it's moving at zero velocity or at hundreds of metres per second.

Our every day experience is that stuff that is moving slows down and stops. But this is actually an oddity of being on the Earth in an atmosphere where there are always frictional forces (with the air or the ground) that try to make you move the same way the ground is moving. You need to separate two concepts in your mind: one is that you will always move in a straight line at a constant velocity unless forces act (that's Newton's first law). The other is that (in the circumstances that happen to be true on the Earth) there are always forces acting unless you are stationary with respect to the surface of the Earth.

 

[Mathivanan]

This isn't right. A body moving at constant velocity has zero acceleration, whether it's moving at zero velocity or at hundreds of metres per second.

Our every day experience is that stuff that is moving slows down and stops. But this is actually an oddity of being on the Earth in an atmosphere where there are always frictional forces (with the air or the ground) that try to make you move the same way the ground is moving. You need to separate two concepts in your mind: one is that you will always move in a straight line at a constant velocity unless forces act (that's Newton's first law). The other is that (in the circumstances that happen to be true on the Earth) there are always forces acting unless you are stationary with respect to the surface of the Earth.

Think of a car at rest. Unless a force acted upon, it cannot move. When you apply force it starts moving against acceleration due to gravity. Depending upon the change in this initial acceleration, the car keeps moving or comes to rest.

 

[ZapperZ]

Think of a car at rest. Unless a force acted upon, it cannot move. When you apply force it starts moving against acceleration due to gravity. Depending upon the change in this initial acceleration, the car keeps moving or or comes to rest.

This is wrong at the elementary level. A force that typically causes a car to move is PERPENDICULAR to the direction of gravity. So the force isn't applied to overcome gravity, but rather because of friction and to overcome inertia.

Now, if you start lifting the car up vertically, then yes, you are opposing the weight of the car, but this isn't how a car normally moves.

I still don't know if you're still asking your original question or whether you've moved on to a different topic. It isn't clear if you've understood the explanation you've been given on your original question.

Zz.

 

[Ibix]

Think of a car at rest. Unless a force acted upon, it cannot move.

More precisely, it cannot start moving without a force if it is initially at rest.

When you apply force it starts moving against acceleration due to gravity.

Really? The acceleration due to gravity is directed vertically downwards. Unless you have a flying car, you are not correct here. The car has to work against friction to move relative to the Earth and air.

Depending upon the change in this initial acceleration, the car keeps moving or or comes to rest.

No. The car will always come back to rest, but this is because of friction. This is the point I was talking about separating in your mind: the car will continue to move at the same speed as long as no force acts on it. But on the Earth there will always be a force acting on it as long as ot moves with respect to the surface of the Earth.

 

[Mathivanan]

More precisely, it cannot start moving without a force if it is initially at rest.
Really? The acceleration due to gravity is directed vertically downwards. Unless you have a flying car, you are not correct here. The car has to work against friction to move relative to the Earth and air.
No. The car will always come back to rest, but this is because of friction. This is the point I was talking about separating in your mind: the car will continue to move at the same speed as long as no force acts on it. But on the Earth there will always be a force acting on it as long as ot moves with respect to the surface of the Earth.

Therefore, the car is at rest due to friction and not due to Earth's gravity.

 

[Mathivanan]

This is wrong at the elementary level. A force that typically causes a car to move is PERPENDICULAR to the direction of gravity. So the force isn't applied to overcome gravity, but rather because of friction and to overcome inertia.

Now, if you start lifting the car up vertically, then yes, you are opposing the weight of the car, but this isn't how a car normally moves.

I still don't know if you're still asking your original question or whether you've moved on to a different topic. It isn't clear if you've understood the explanation you've been given on your original question.

Zz.

I began with v=u+at and still continuing with that.

 

[ZapperZ]

I began with v=u+at and still continuing with that.

This doesn't explain anything.

Zz.

 

[Ibix]

Therefore, the car is at rest due to friction and not due to Earth's gravity.

Not quite. It moves at the velocity it is moving at because it was already moving at that velocity. If some force pushes it into changing its motion then, on the surface of the Earth, a frictional force will always appear to resist any motion relative to the surface.

 

[Ibix]

I began with v=u+at and still continuing with that.

I think your problem is distinguishing between forces and accelerations.

 

[Mathivanan]

This isn't right. A body moving at constant velocity has zero acceleration, whether it's moving at zero velocity or at hundreds of metres per second.

Our every day experience is that stuff that is moving slows down and stops. But this is actually an oddity of being on the Earth in an atmosphere where there are always frictional forces (with the air or the ground) that try to make you move the same way the ground is moving. You need to separate two concepts in your mind: one is that you will always move in a straight line at a constant velocity unless forces act (that's Newton's first law). The other is that (in the circumstances that happen to be true on the Earth) there are always forces acting unless you are stationary with respect to the surface of the Earth.

What is precisely 'oddity of being on the Earth'?

 

[Ibix]

What is precisely 'oddity of being on the Earth'?

The oddity of being on the Earth is that you're surrounded by matter in large quantities, and if you want to move relative to it you need to work to push it out of the way. That isn't anything to do with motion in its own right. Separating the concepts of "moving" and "having to shove the air out of the way if you want to move relative to it" was one of Newton's great insights (edit: or Galileo's I suppose, although Newton developed the concept into his laws of motion).

 

[Mathivanan]

The oddity of being on the Earth is that you're surrounded by matter in large quantities, and if you want to move relative to it you need to work to push it out of the way. That isn't anything to do with motion in its own right. Separating the concepts of "moving" and "having to shove the air out of the way if you want to move relative to it" was one of Newton's great insights (edit: or Galileo's I suppose, although Newton developed the concept into his laws of motion).

I like that:surrounded by matter in large quantities.

 

[Mathivanan]

Not quite. It moves at the velocity it is moving at because it was already moving at that velocity. If some force pushes it into changing its motion then, on the surface of the Earth, a frictional force will always appear to resist any motion relative to the surface.

Apple fell down from the tree due to Earth's gravity. I could pick that apple because of frictional force, otherwise it should have gone down to the center of earth.

 

[jbriggs444]

Apple fell down from the tree due to Earth's gravity. I could pick that apple because of frictional force, otherwise it should have gone down to the center of earth.

Relevance, please?

A car moving down the highway at 50 miles per hour subject to zero net force will have a constant acceleration of zero despite the fact that it is not at rest in the ground frame.

 

[Dale]

What I thought is: a body is said to have zero acceleration when it is either at rest or comes to rest if it's moving;

You seem to be confusing acceleration and velocity. What you wrote is completely false. It would be essentially correct to say "a body is said to have zero velocity when it is either at rest or comes to rest if it's moving"

In the equation v=u+at, when a=0, the body moves with a constant velocity. Can we say that the body is moving with zero acceleration? If it is how a body can move with constant velocity without acceleration.

Yes. If a=0 then it moves at constant speed in a straight line per Newton's first law. Such motion is called "inertial".

It should have a positive acceleration to move with constant velocity. Hence 'a' cannot be zero.

This is not correct. Also, a is a vector so the designation of "positive acceleration" doesn't even make sense generally.

Therefore, there is something wrong with my understanding. In the equation, 'a' is not simply acceleration but rather a change in acceleration or Δa. As a body cannot be moved without acceleration

Yes, your understanding is wrong. The "a" is simply acceleration. Your belief that a body cannot be moved without acceleration is wrong. A body cannot be moved without velocity, but velocity can be nonzero while acceleration is zero. Again, such motion is called "inertial".

 

[Mathivanan]

Relevance, please?

A car moving down the highway at 50 miles per hour subject to zero net force will have a constant acceleration of zero despite the fact that it is not at rest in the ground frame.

Has the driver taken off their leg from the accelerator?

 

[Mathivanan]

You seem to be confusing acceleration and velocity. What you wrote is completely false. It would be essentially correct to say "a body is said to have zero velocity when it is either at rest or comes to rest if it's moving"

Yes. If a=0 then it moves at constant speed in a straight line per Newton's first law. Such motion is called "inertial".

This is not correct. Also, a is a vector so the designation of "positive acceleration" doesn't even make sense generally.

Yes, your understanding is wrong. The a is simply acceleration. Your belief that a body cannot be moved without acceleration is wrong. A body cannot be moved without velocity, but velocity can be nonzero while acceleration is zero. Again, such motion is called "inertial".

You need a force to move a body and that force is mass*acceleration.

 

[Dale]

You need a force to move a body.

No, you don't. See Newton's first law.

Please re-read my corrections above to understand where you are going wrong, and make your next post responsive to the specific points raised.

 

[jbriggs444]

Has the driver taken off their leg from the accelerator?

I said zero net force. Can you tell us what that means?

 

[Clausen]

Isnt zero a constant? What is the confusion here?

Perhaps the OP is confused between zero acceleration as a particular case of constant acceleration.

 

[PeterO]

What I thought is: a body is said to have zero acceleration when it is either at rest or comes to rest if it's moving; it is because acceleration due to gravity.

Just taking your statement one piece at a time.
NO - a body is said to have zero acceleration if its velocity is constant. It may be at rest (and remaining at rest) or continuing at constant velocity.
Moving at constant velocity is obviously easy to achieve - drivers of cars manage that everyday on the straight, flat, highways of America when they set Cruise Control and sit back traveling a t a constant 50 mph.

Your other option " ... comes to rest if it's moving;" NO again, If it was moving, and then comes to rest, it has definitely had an acceleration other than zero.

The last bit: "it is because acceleration due to gravity" is puzzling. Are you thinking about an object being thrown vertically up? it slows down, stops, then comes back down again.
If you are thinking of that then again NO. if you were to throw a ball vertically up, then catch it when it gets back to your hand, then for all the time from when it left your hand to when you hold it again, its acceleration was 9.8 metres per second per second (at all times - even when it stopped at the top of the flight).

 

[PeterO]

... If it is how a body can move with constant velocity without acceleration. It should have a positive acceleration to move with constant velocity. Hence 'a' cannot be zero. Therefore, there is something wrong with my understanding...

Yes - there is something wrong.
Acceleration is the rate of change of velocity (speed and direction) If we consider motion in a straight line, the direction part can be defined as positive or negative.
Position, velocity and acceleration are each particular measures of a body. Let's consider morning traffic on a freeway - as seen by an observer (you) on an overhead bridge. Position zero is directly below you - positive direction in in the direction you are looking while negative direction is behind you.
Time zero is when you open your eyes. (you have already walked onto the bridge, faced along the freeway and closed your eyes in preparation).
At time zero (when you open your eyes) you see many cars traveling in the positive direction, and many more traveling in a negative direction. Hopefully, none of them will have zero velocity. However, some of them may have been at position zero the instant you opened your eyes (but didn't stay there)
Many of the cars will have had zero acceleration - all those traveling at constant speed in the direction they are heading.
Some cars may have positive acceleration: includes those traveling in a positive direction (away from you in the direction you are looking) and speeding up, but also those traveling towards you (as you look) and slowing down.
Some cars may have negative acceleration: includes those traveling in a positive direction (away from you in the direction you are looking) and slowing down, but also those traveling towards you (as you look) and speeding up.
Those positive and negative accelerations might be constant but don't have to be.
Every vehicle changing its speed (even slightly) is accelerating. All those traveling at constant speed have zero acceleration. (NOTE: I can use the term speed here because we are only considering motion on a straight section of freeway)

I hope that explains some of this.

 

[PeterO]

In the equation v=u+at, u=5 m/sec and a=0, then v=5 m/sec. That means the body is moving with a constant velocity of 5 m/sec. In a velocity-time graph, the equation produces a straight horizontal line. Some texts say the body is moving with zero acceleration and others say it is moving with constant acceleration. Which is correct?

Can you please check those texts. I would think it is more common for some texts to say the body is moving with constant acceleration, while others say it is moving with constant velocity. (or perhaps constant speed, because they are considering motion in a straight line, and always in the one direction).
Sure zero acceleration is an example of constant acceleration, but it is such a special case that we usually like to emphasis that value of zero.