Calculating Velocity of Constantly Accelerating Object: A Physics Lesson

In summary, the conversation discusses the formula for calculating velocity of an object with constant acceleration and the concept of velocity addition in special relativity. The participants also mention the importance of using reliable sources, such as books, for learning physics rather than relying on websites.
  • #1
divito
6
0
If we have an object that is theoretically set to accelerate constantly for an unknown amount of time (disregarding the issues that alone brings up), what formula would be used to calculate its velocity? I know we can determine final velocity for after t amount of time, but would velocity-addition be more appropriate?

I'm attempting to teach myself physics and while I know of velocity-addition and final velocity, I haven't found a place that indicates under cases to use them.

Does anyone have a site they personally know that is any good for physics instruction?
 
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  • #2
What do you mean by velocity addition?

[tex]a = \frac{d^2 x}{dt^2} = \frac{dv}{dt}[/tex]

treat as differentials

[tex] \int_{t'=0}^{t'=t}a dt' = \int_{v(0)=v_0}^{v(t)} dv[/tex]

gives an equation for velocity based on an initial velocity

[tex] v(t) = v_0 + at[/tex]

If you want to get rid of the time dependencies then solve for t

[tex] t = (v - v_0)/a[/tex]

Then because you know that (from the mean value theorem if you have done it)

[tex] x = \vec{v}t = (1/2)(v_0 + v)t[/tex]

Where we have already figured out t that.

[tex] x = (v+v_0)(v-v_0)/2a[/tex]

So solve for velocity

[tex] v^2 = v_0^2 + 2ax[/tex]

I don't think that relying on websites to learn physics is such a good idea. I would see what the library has in terms of books. I think that Randall Knight has a pretty good introductory physics book if your library has it.
 
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  • #4
Oh, I see what you are asking. You are wondering whether if some acceleration is applied to an object for long enough, do you have to consider relativistic effects? I guess the short answer would be yes. The thing is though that as the particles velocity increases, its mass will increase too, and so whatever is forcing it will have a harder and harder time accelerating it. There will, in a way, be a limiting acceleration (and therefore a limiting velocity) that will depend on the force and the mass.

The safest thing to do with relativity is to use the equations that always work, which are conservation of energy, and conservation of momentum. For example, rather than F=ma, which is true only in general (i.e. non-relativistic cases) you should use F = dp/dt.

Do you have a specific example, or are you just wondering?
 
  • #5
No real specific example. It's just, I read about these formulas and such, but haven't found a place that really discusses to what, where and why they're used.
 
  • #6
Okay. If you haven't figured out by now, the velocity addition formulas relate to special relativity. My previous suggestion still stands of finding a published book, Knight even covers special relativity if you can find the big book with all volumes in one, rather than trusting internet Joe Schmo.
 
  • #7
Mindscrape said:
Okay. If you haven't figured out by now, the velocity addition formulas relate to special relativity. My previous suggestion still stands of finding a published book, Knight even covers special relativity if you can find the big book with all volumes in one, rather than trusting internet Joe Schmo.

Yup, I've been reading a lot about GR and SR recently. But I'll start perusing for books. Thanks :D
 
  • #8
Mindscrape is, of course, right. But here's a Schmo who seems to know what he's talking about with some graphs for a preview. Can you check that he is right?
http://physics.nmt.edu/~raymond/classes/ph13xbook/node59.html [Broken]
 
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1. How do you calculate the velocity of a constantly accelerating object?

To calculate the velocity of a constantly accelerating object, you will need to use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Simply plug in the values for each variable and solve for v to find the velocity.

2. What is the difference between velocity and acceleration?

Velocity refers to the rate of change of an object's position over time, while acceleration refers to the rate of change of an object's velocity over time. In simpler terms, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much an object's velocity is changing.

3. Can an object have a constant acceleration?

Yes, an object can have a constant acceleration if its velocity is changing at a constant rate. This means that the object's acceleration remains the same throughout its motion, regardless of the time or distance traveled.

4. How does an object's mass affect its acceleration?

An object's mass does not directly affect its acceleration. However, a larger mass may require more force to accelerate at the same rate as a smaller mass. This is described by Newton's second law of motion: F = ma, where F is the force applied, m is the mass, and a is the acceleration.

5. Can an object have a negative acceleration?

Yes, an object can have a negative acceleration. This means that the object is slowing down in the direction of its motion. Negative acceleration is also known as deceleration or retardation. In this case, the final velocity will be less than the initial velocity, resulting in a negative value for acceleration.

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