Joules to do something If my very limited understanding is correct, then, not accounting for gravity:
1 Newton can move 1 kilogram 1m
But, can 2 Newtons move 1 kilogram 2 meters?
Is this because 1 Newton = acceleration of 1/ms, so, 2 Newtons would result in a speed of 2 m/s? Or would it be 1 m/s lasting twice as long?
So what does a joule do: accelerate or just move?
 A: You have an incorrect understanding of forces, accelerations and velocities. A force of 1 Newton can accelerate a 1 kg mass at a rate of 1 m/s/s (often written as 1 m/s$^2$). A force of 2 Newtons can accelerate the same 1 kg mass at a rate of 2 m/s/s.
We relate the accelerations, velocities and positions via the kinematic equations; for this case we can use
$$
x_{new}(t)=x_{old}+vt+\frac12at^2
$$
where the $old$ subscript is the initial position and the $new$ subscript indicates where we will be after $t$ seconds due to an initial velocity, $v$, and acceleration, $a$. If we consider the object as initially stationary, $v=0$, and at position $x_{old}=0$, then in 1 second the two forces give us total distances of
$$
x_{new}(t=1\,{\rm s})=\begin{cases}\frac12\,{\rm m} & F=1\,{\rm N} \\ 1\,{\rm m} & F=2\,{\rm N}\end{cases}
$$
After 2 seconds, we have
$$
x_{new}(t=2\,{\rm s})=\begin{cases}2\,{\rm m} & F=1\,{\rm N} \\ 4\,{\rm m} & F=2\,{\rm N}\end{cases}
$$
The velocities after 1 second would be
$$
v_{new}=v_{old}+at=\begin{cases}1\,{\rm m/s} & F=1\,{\rm N} \\ 2\,{\rm m/s} & F=2\,{\rm N}\end{cases}
$$
So to answer your questions about distances and speeds, you really need to know how long the force is applied to the object.
The joule is the measure of the work the force does after moving the object some height.
A: 
1 Newton can move 1 kilogram 1m
But, can 2 Newtons move 1 kilogram 2 meters?
Is this because 1 Newton = acceleration of 1/ms, so, 2 Newtons would
  result in a speed of 2m/s? Or would it be 1m/s lasting twice as long?
So what does a joule do: accelerate or just move?

A joule does not accelerate, it is the unit, the measure both of 


*

*kinetic energy (that a body has when it has been accelerated and has velocity) and the measure of 

*work done against a force


1 N (newton) does not move but accelerates 1 Kg by 1 m/s every second, using the correct units: $1 m/s^2$. 2 N (newtons) give 1Kg double acceleration:  $2 m/s^2$. Gravity is a Force of ca. 


*

*10 N and accelerates 1 Kg by $10m/s^2$ (and not, as you write, 1(0) /ms, I edited your post by I left that, as I cannot know if it is a typo or what units you really wanted to write). That means that every second its velocity increases by 10 m/s. If it lasts for a second, then speed will be 10 m/s and KE 50 joules and it will travel a distance of 5m, if it lasts two seconds its speed will be 20 m/s and its KE 200 joules, and so on.


The energy these body acquires is measured in Joules and depends on the time the force acts on the bodies. This is the case of 1 (or more) Kg of mass that falls to the ground because of gravity for 1 (or more seconds)


*

*If on the contrary, you want to lift up a weight of 1Kg, then you do not accelerate the body but you move it or, better displace it, it gains no speed because you are doing work, you are working against a force (gravity), and with the same amount of energy (joules) you can lift a 

*k-Kg body by 1m, or a 

*.5k-kg-body by 2m, or a 

*2k-Kg body by .5m


That is because joules are the product of force by displacement: (Ke) = Work = $\rightarrow = F . d$, so  $\rightarrow k *1 = .5k *2 = 2k *.5$
If you want to lift that body back to the height of 5m, you must apply a force of 10N by 5 metres, and spend the 50 joules of energy it gained falling down, and that because you fight against a force of 10N over the distance of 5m-
In conclusion: gravity accelerates a body, accelerates it  and gives it energy (joules), if you want to lift a body, you spend energy (joules) to displace/ lift it up, in this case you might say, in approximate language, that: 'joules make a body move*
A: $F=ma$ so $1N$ accelerates a $1kg$ mass by $1m/s^2$.
It does not mean that it will only move 1 metre.
