Can an object accelerate at a constant pace forever?

In summary, an object accelerating at a rate of 6m/s^2 can continue to accelerate forever without reaching the speed of light if there is an endless supply of fuel. The observer on the object would feel a constant acceleration and nothing else. The time it takes for a ball to fall from the top of the object to the bottom would remain the same regardless of the object's velocity. If the object is traveling at a velocity of 299,792,457m/s, nothing significant would happen as speed is relative. However, if the acceleration is measured in a given inertial frame, the object cannot continue to accelerate indefinitely.
  • #1
Zaephou
4
1
Considering special relativity, let us take an object accelerating at a rate of 6m/s^2. Let's say that this object is large enough for an observer to securely stand on it while it is accelerating.

Would this object be able to accelerate at this rate forever without reaching the speed of light, and if so, what affects would the observer feel as the velocity reaches the speed of light?

Side question: Let's say a ball is held up 1m above the surface of this object, and is let go. Would the time the ball takes to reach the surface differ if the velocity of the object was at 25% the speed of light compared to 75% the speed of light?

Also, what would happen (if anything), if the object is traveling at a velocity of 299,792,457m/s (one less that the speed of light)?
 
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  • #2
Zaephou said:
Considering special relativity, let us take an object accelerating at a rate of 6m/s^2.
Let's assume that's a proper acceleration, as measured by an accelerometer on the object.
Zaephou said:
Let's say that this object is large enough for an observer to securely stand on it while it is accelerating.

Would this object be able to accelerate at this rate forever without reaching the speed of light, and if so, what affects would the observer feel as the velocity reaches the speed of light?
If fuel doesn't run out yes. And if we assume an empty space without any gas, dust, rocks or background radiation then the observer will just feel a constant acceleration forever, nothing else.
Zaephou said:
Side question: Let's say a ball is held up 1m above the surface of this object, and is let go. Would the time the ball takes to reach the surface differ if the velocity of the object was at 25% the speed of light compared to 75% the speed of light?
You may want to come up with some other question that doesn't imply gravity. Otherwise all physical processes take the usual amount of time, measured with the observe's clock.
Zaephou said:
Also, what would happen (if anything), if the object is traveling at a velocity of 299,792,457m/s (one less that the speed of light)?
Nothing, speed is relative. You are currently traveling at almost the speed of light relative to some high-energy cosmic particle.
 
  • #3
If, by constant acceleration you mean "as measured in a given inertial frame", the answer is no, it cannot continue indefinitely. If you mean, can a rocket accelerate such that objects inside experience constant g-force forever, the answer is yes (barring the practical constraints mentioned in Vitro's post). In this case, the time for an object to fall from from the top of the rocket to the bottom, as measured by the bottom (there are some subtleties here, which I will gloss over for the moment; suffice it to say, you have to define carefully what yo mean by this because there is time dilation of clocks at the bottom of the rocket compared to the top), will remain the same, always. Specifically, even if the the rocket is moving 1 cm/sec less that c per some initial inertial frame, the top to bottom fall measurement as done in the rocket will be the same as when the rocket was moving at 1 meter/sec per this initial inertial frame.
 

1. Can an object accelerate at a constant pace forever?

No, an object cannot accelerate at a constant pace forever. This is because acceleration is the rate of change of velocity, and in order for an object to continue accelerating, its velocity would have to keep increasing at a constant rate. However, this is not possible as there are factors such as air resistance and friction that would eventually slow down the object's acceleration.

2. What is the difference between constant speed and constant acceleration?

Constant speed refers to the rate at which an object is moving, while constant acceleration refers to the rate at which its velocity (speed and direction) is changing. An object can have a constant speed but still be accelerating if its direction is changing, such as in circular motion. On the other hand, an object can have a constant acceleration even if its speed is changing, as long as the rate of change in velocity remains constant.

3. Can an object maintain a constant acceleration without any external forces acting on it?

No, an object cannot maintain a constant acceleration without any external forces acting on it. This is because according to Newton's Second Law of Motion, an object will only accelerate if there is a net force acting on it. Without any external forces, the object would continue to move at a constant velocity.

4. Is there a limit to how fast an object can accelerate?

Yes, there is a limit to how fast an object can accelerate. This limit is called the speed of light, which is approximately 299,792,458 meters per second. According to Einstein's theory of relativity, as an object approaches the speed of light, its mass increases and it requires more and more energy to continue accelerating.

5. Can an object accelerate indefinitely in a vacuum?

In a vacuum, where there is no air resistance or other external forces, an object can theoretically continue accelerating indefinitely. However, as it approaches the speed of light, the amount of energy required to accelerate the object further would become infinite. Therefore, in practical terms, an object cannot accelerate indefinitely even in a vacuum.

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