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Understanding Velocity - Time graphs
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Ivana Minz
May 9, 2013, 3:39:46 AM5/9/13
to
What would the graphs of the following to cases look like?
1. The body is accelerated non uniformly along a line and then continues
moving with non constant acceleration along the opposite direction
i.e. back to where it started from.
2. The body is accelerated non uniformly along a line and return to
where it first started undergoing non uniform retardation taking an
equal amount of time as it had taken to reach the point where it
arrived.
1. The body is accelerated non uniformly along a line and then continues
moving with non constant acceleration along the opposite direction
i.e. back to where it started from.
2. The body is accelerated non uniformly along a line and return to
where it first started undergoing non uniform retardation taking an
equal amount of time as it had taken to reach the point where it
arrived.
Mike Fontenot
May 10, 2013, 2:45:40 AM5/10/13
to
you will have to do a numerical integration. It's described here:
https://sites.google.com/site/cadoequation/cado-reference-frame
and here:
M. L. Fontenot, "Accelerated Observers in Special Relativity", PHYSICS
ESSAYS, December 1999, p629.
--
Mike Fontenot
Jos Bergervoet
May 11, 2013, 3:59:00 PM5/11/13
to
On 5/10/2013 8:45 AM, Mike Fontenot wrote:
> On 05/09/2013 01:39 AM, Ivana Minz wrote:
>
>> What would the graphs of the following to cases look like?
>>
>> 1. The body is accelerated non uniformly along a line and then continues
>> moving with non constant acceleration along the opposite direction
>> i.e. back to where it started from.
>>
>> 2. The body is accelerated non uniformly along a line and return to
>> where it first started undergoing non uniform retardation taking an
>> equal amount of time as it had taken to reach the point where it
>> arrived.
>
> Completely general acceleration profiles can be handled, although in general
> you will have to do a numerical integration. It's described here:
>
> https://sites.google.com/site/cadoequation/cado-reference-frame
You do not need a specific reference frame. All
> On 05/09/2013 01:39 AM, Ivana Minz wrote:
>
>> What would the graphs of the following to cases look like?
>>
>> 1. The body is accelerated non uniformly along a line and then continues
>> moving with non constant acceleration along the opposite direction
>> i.e. back to where it started from.
>>
>> 2. The body is accelerated non uniformly along a line and return to
>> where it first started undergoing non uniform retardation taking an
>> equal amount of time as it had taken to reach the point where it
>> arrived.
>
> Completely general acceleration profiles can be handled, although in general
> you will have to do a numerical integration. It's described here:
>
> https://sites.google.com/site/cadoequation/cado-reference-frame
reference frames (and in GR any coordinate system)
is allowed to do your calculations and all will
agree on the events that take place.
In particular, to answer the question of OP one
would need to know what coordinates are used!
Presumably, what is meant is to look at things in
a fixed inertial frame. The graphs asked for would
look like a certain class of wavy lines (it's
obviously a homework problem to find those, so
we should not elaborate on it.)
But one could choose coordinates for a co-moving
observer, where the frame at any moment is given
by the Rindler coordinates for the acceleration
at that moment. For that special choice, the
graph would be a perfectly straight vertical line.
(NB: To give this answer might be dangerous for a
homework problem, depending on the teacher..)
--
Jos
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