Where does the activation energy for ATP come from? ATP provides the energy for energy-consuming endergonic reactions, for example to power a molecular motor.
The reaction is:
$$\text{ATP}+\text{H}_2\text{O}\to \text{ADP}+\text{P}_i+\text{free energy}$$
This reaction needs activation energy in order to take place. This is good because otherwise, all energy would be released immediately and it could not function as an energy storage.

Now my question:
How can a molecular motor (or any other energy consuming protein) access the energy of ATP, when it gets near? 
In my current understanding the activation energy can not come from the molecular motor, because this needs energy, and does not provide energy.
One analogy:
One has a matchstick (stored energy), and a droplet of water. You want to vaporize the water, but this is not possible without lightening the matchstick (activation energy), which the water can not provide.
But one can observe that our body can access this energy. How is this possible?
And furthermore:
Can the molecular motor access $\Delta G^0$, or $\Delta G^0 + \Delta G^* $?
 A: The reaction doesn't need activation energy to occur. The lower energy state is still favorable, and so the reaction will take place due to thermal fluctuations (probably at the rate predicted by some sort of Arrhenius equation); however, it will occur much too slowly to be of any use. This is why enzymes are so important. Specifically, a class of molecules called "ATPases" can be used to lower the activation energy$^*$, and thus cause the reaction to occur at a faster rate.
In fact, motors serve as ATPases. You will notice that ATP molecules need to bind to specific sites on the motor before force generation can be performed by the motor. ATP binds, the activation energy is lowered, and so the reaction is more likely to occur. The energy that will become available will just be $\Delta G^0$, which makes sense; we wouldn't want our ATPase to lower the amount of energy obtained by the reaction.

$^*$I will admit, I did not know much of the specifics of how this is done, but I found a simple explanation here, although it looks like they are not taking thermal fluctuations into account.

Although ATP hydrolysis is a favorable reaction, ATP does not breakdown on its own. This is because the activation energy required for the hydrolysis of ATP is high enough that ATP hydrolysis does not take place without an enzyme called ATPase. The lone pair of electrons on the oxygen of a water molecule perform a nucleophilic attack on the terminal phosphate group. However, these electrons have a negative charge and are strongly repelled by the negative charges on the phosphate molecule.
ATPases help overcome this repulsion by surrounding the ATP molecule with positive ions that interact with the negative charged ions on the phosphate molecule, allowing hydrolysis to take place. Hence, ATPases lowers the activation energy required for the reaction to occur.

