Can an object be accelerating and yet -not- moving?

@Finn dAbuzz,

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Do you believe that a decision made through intuition has simply invoked a random decision generator?

Don't think that's what Max meant but it did sound that way didn't iot

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….isn't very effective for problems much more complex than "Do I move…...into that clearing ahead?"

Disagree, think it's much more profound. But don't want to start a war

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or "Which person do I ask to watch my baggage while I go to the restroom?"

Now this might require some pretty sharp judgement depending on many factors not accessible to the conscious--nonetheless as you say, comes quick

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but something is going on in the mind…..beyond spinning a wheel……...

Yes Buzz, much much more

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@Finn dAbuzz,

No. A decision made through intuition is often worse than a random decision generator. Intuition encompasses our fears, our desires and our prejudices.

People acting on intuition are acting irrationally.

I avoid making a decision based on intuition on anything important except for the time where a quick decision is more important than a logical one. By that I mean that if I can't come up for a logically defensible reason for a feeling I have, I ignore the feeling.

So many irrational things that people do and believe are based on what they feel is right even though they can't support it logically.

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@raprap,

What do you mean by a boundary condition? I've always thought of it as an instantaneous condition. Take a simple graph paper with a slope, for example, where there is plot of velocity with respect to time, with a nonzero slope passing the x-intercept, where the acceleration remains constant throughout the run. Therefore, when the instantaneous velocity is zero (hitting the x-intercept), the object in motion is changing from from one direction to another direction (+ to - or - to +) depending on if the slope is positive or negative. It can be from positive direction of motion to the negative direction, or vice versa. Only at such intercept, where v is instantaneously zero and such non-zero slope is constant therefore at that instantaneous movement there is a positive or negative non-zero acceleration, arbitrary to the sign of the slope.

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@Falco,

Definition Boundary Condition

http://www.thefreedictionary.com/boundary+condition

Rap

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@raprap,

I understand the definition of boundary condition, but I think it is inaccurate in describing an instance where an object is instantaneously at rest, v(t)=0, but is either on the verge of starting to move or is turning around and changing direction. At such an instantaneous moment, the velocity is zero (ds/dt=0), but the acceleration is nonzero (dv/dt Not Equal

0).
There aren't any boundaries involved or finding the area under the a line involved. Using a position vs. time graph you simply need to find the equation to a tangent line and find the value at the point of interest to find the instantaneous vleocity, and in a similar manner the tangent of a velocity-time graph represents instantaneous acceleration.
Take the trajectory of the ball for example,
a = dv/dt = -g (using the convention that upwards is positive),
v = -g\int{dt} + C
v = -gt + v0

where v0 is the initial velocity, and we let this to be positive since it was tossed upwards.

Plotting as a function of t, v becomes smaller, until at some point, -gt + v0 = zero. But with constant acceleration of -g. In the curve of velocity vs. time. At some time, t, the instantaneous velocity is zero. The acceleration is the slope of the velocity curve at time t.

Still fail to see how the boundary condition applies, unless I'm missing something.

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@Falco,

Evidently then the math establishes it. Yet Her "creation" is not necessarily tied to the math (man's creation) while Intuition stubbornly insists on that moment of zero acceleration

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@dalehileman,

If an object at zero velocity has zero acceleration, it can never move. All stationary objects that are set into motion have an acceleration applied to them while they are stationary.

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@Falco,

Falco wrote:

Still fail to see how the boundary condition applies, unless I'm missing something.

Your issue here is a semantical one, not mathematical. Substitute " initial condition" for "boundary contition" and you may feel better. Raprap (I believe) referred to the fundamental theorem of calculus (the integral as the anti derivative). The issues here are simply the constants associated with the two integrations of the (variable or constant) acceleration. One is the initial position, the other is the initial velocity.

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@engineer,

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If an object at zero velocity has zero acceleration, it can never move.

I'm neither physicist nor mathematician, can only respond it's counterintuitive

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All stationary objects that are set into motion have an acceleration applied to them while they are stationary.

Being a rank amateur at this sort of thing capable of only the most literal interpretation, it seems that this sentence has several possible meanings so perhaps ought to be reworded for the benefit of the Intellectually Disadvantaged (me)

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@dalehileman,

Think of it this way - imagine a stationary object that is not moving. Now imagine that you push it - i.e. apply a force to it - at the instant you apply the force the object starts to move - it is accelerating and the acceleration is proportional to the force applied and inversely proportional to the mass of the object (F = M x A, or eqivalently, A = F/M).

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@georgeob1,

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Think of it this way - imagine a stationary object that is not moving.

Yes that's usually how I imagine a stationary object

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Now imagine that you push it …….starts to move - it is accelerating……... (F = M x A, or eqivalently, A = F/M).

Of course, that's how I had always understood it. But that doesn't explain how it's accelerating when it's stationary

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@dalehileman,

Acceleration is the rate of change of velocity. Velocity can be zero and changing(in the ball's case going from positive velocity to negative velocity at the peak of the trajectory), in which case there is an acceleration.
In other words, if magnitude of velocity is zero, and the direction is changing, then the object is accelerating.
In addition to this, consider an object being spun around at a constant speed (note I did not say velocity) in a circle. Because the direction is changing, the object is accelerating, angular acceleration in this case. Actually in this case of an object traveling around in a circle, the magnitude of its average velocity is always zero, because it has no displacement, returning always to its starting point.

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@dalehileman,

dalehileman wrote:

But that doesn't explain how it's accelerating when it's stationary

Thanks for pointing out my redundant phrase.

What contradiction can there be in the idea of an accelerating object that has a zero velocity? Engineer provided a perfectly clear example with a vertically thrown ball on the verge of reversing its trajectory. Clearly gravity is still operating on the ball at the moment when it is no longer moving, so the idea of an unopposed force applied to an object with zero velocity shouldn't be a problem.

I can tell you, from my own experience, that an aircraft in vertical flight will slow down and (if one is gentle on the controls), stop, and the nose will fall vertically down. Moreover one experiences near zero "g" at that moment confirming the acceleration of the aircraft cancelling out some or most of the gravity acceleration.

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@georgeob1,

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What contradiction can there be in the idea of an accelerating object that has a zero velocity?

Intuition (mine anyhow) insists that when it's stopped it isn't accelerating

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@dalehileman,

Do you understand or acknowledge that the slope of a line can be increasing even though, at that moment, it is (say) horizontal? There are infinitely many points on the line between the present one and any nearby point, just as there are infinitely many moments in time between now and a second later. Moreover there are infinitely many real numbers between any two coordinate values or measures of time with which to describe them. All involve continuous processes and measures that are fundamental to mathematics and science. There are, at a subatomic level, minimum quantities (quanta) of mass, energy and momentum, but not time and space. Even there the nature of mass & energy becomes complex and the descriptions of it as involving waves or mass is essentially metaphorical.

How about a falling rock accelerating under the force of gravity. If it's velocity at some instant is (say) v, is it accelerating to a greater speed due to gravity ? All of modern mechanics is based on the observation that this is true. What difference is there if the initial velocity, v, is zero?

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@maxdancona,

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By that I mean that if I can't come up for a logically defensible reason for a feeling I have, I ignore the feeling.

I like that. Helps one avoid mistakes.

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@aspvenom,

aspvenom wrote:

Because the direction is changing, the object is accelerating, angular acceleration in this case.

The math here is really not as not nearly as difficult as you all are making it.

An object going at constant speed around a circle is not experiencing angular acceleration. It is experiencing linear acceleration (i.e. acceleration in a direction). Angular acceleration is the result of a torque meaning that the speed would be changing.

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@maxdancona,

Well, there isn't linear velocity, only angular... I was just trying to make it sensible to Dale. I have failed at that. Sad

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@georgeob1,

georgeob1 wrote:

Falco wrote:

Still fail to see how the boundary condition applies, unless I'm missing something.

Your issue here is a semantical one, not mathematical. Substitute " initial condition" for "boundary contition" and you may feel better. Raprap (I believe) referred to the fundamental theorem of calculus (the integral as the anti derivative). The issues here are simply the constants associated with the two integrations of the (variable or constant) acceleration. One is the initial position, the other is the initial velocity.

That makes more sense. I appreciate your taking the time in explaining that.

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@aspvenom,

You are incorrect aspvenom.

The linear velocity is the speed and the direction of the object at any given time. An object going at a constant speed in a circular path absolutely has a speed and a direction at any given time.

So yes, this object has a non-zero linear velocity.

The linear acceleration is the change in the linear velocity. Since the direction the object is moving is changing, there is absolutely a linear acceleration.

The angular velocity is the angular speed (i.e. the number of radians the object is travelling around the circle per second) with a direction along the axis of rotation. There is an angular velocity for this object at constant speed around a circular path, but it isn't changing because at constant speed the object travels the same number of radians each second, and since the direction is the axis of rotation it doesn't change.

And of course, since the angular velocity isn't changing, the angular acceleration for constant speed circular motion is zero. If the speed of the object is changing, then that would mean a non-zero angular acceleration.

This is math. There is a right answer. If your intuition doesn't match the right answer, then your intuition is wrong.

Actually, this is rather simple math. These answers are things you probably learned and forgot in high school.

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Can an object be accelerating and yet -not- moving?

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