Whether constant acceleration and zero acceleration are the same

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Discussion Overview

The discussion revolves around the concepts of constant acceleration and zero acceleration, particularly in the context of motion described by the equation v=u+at. Participants explore whether these two terms can be considered equivalent and the implications of zero acceleration in relation to constant velocity. The scope includes theoretical interpretations and conceptual clarifications.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that when acceleration (a) is zero, the body moves with a constant velocity, suggesting that zero acceleration can be viewed as a special case of constant acceleration.
  • Others propose that constant acceleration typically implies a non-zero value, leading to confusion about the terminology used in different texts.
  • One participant notes that zero is indeed a constant, questioning the need to qualify acceleration as constant when it can be zero.
  • Another participant emphasizes that constant acceleration means the acceleration does not change over time, which can include zero acceleration.
  • Some participants express that the distinction between zero and non-zero acceleration is significant in natural language, though mathematically it may not be.
  • There are mentions of the "suvat" equations, which apply to constant acceleration but do not hold for cases of varying acceleration.
  • One participant reflects on the implications of Newton's first law, stating that a body will move in a straight line at constant velocity unless acted upon by forces.
  • Another participant challenges the idea that a body cannot move without acceleration, suggesting that the initial acceleration is necessary for motion.
  • Some participants highlight the everyday experience of motion, noting that external forces often influence the perception of acceleration and velocity.

Areas of Agreement / Disagreement

Participants express differing views on whether zero acceleration can be classified as constant acceleration. While some see them as equivalent, others maintain that constant acceleration typically implies a non-zero value. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are unresolved assumptions regarding the definitions of acceleration and the implications of constant versus zero acceleration. The discussion also touches on the applicability of certain equations under varying conditions of acceleration.

  • #31
Dale said:
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.
 
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  • #32
Mathivanan said:
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.
 
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  • #33
Mathivanan said:
Has the driver taken off their leg from the accelerator?
I said zero net force. Can you tell us what that means?
 
  • #34
Dale said:
Isnt zero a constant? What is the confusion here?

Perhaps the OP is confused between zero acceleration as a particular case of constant acceleration.
 
  • #35
Mathivanan said:
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).
 
  • #36
Mathivanan said:
... 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.
 
  • #37
Mathivanan said:
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.
 

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