This phenomenon is not unusual. Most marathoners actually sprint across that line with all of their remaining energy. It seems that there is a special brain event that occurs called 'The X-Spot', which is when the brain releases a flood of endorphins (and other chemicals) that provides them with the energy needed to accelerate.
This X-Spot is indicative of how powerful a force goal attainment can be. The magic moment occurs when the brain realizes that success is not only possible - but probable. Positive psychological research demonstrates that this reaction of the brain occurs not just when someone sees the finish line of a goal, but the moment they realize the probability they will succeed. This means that it is our perception of our success that drives our brain to release chemicals that will accelerate our success.
To manage this process though, we need to manage our perceptions.
1. Clarify the goal. We must have a clear and defined goal that we are targeting. Our brains are constantly mapping out action paths we can take and assessing how close we are to achieving our goals. However, the brain can't work effectively for us if it is unsure about what it is that we are trying to accomplish. The clearer we are about the 'what' we want to achieve the less energy we waste on unnecessary course corrections along the way.
2. Make it Closer. The closer we are to achieving something, the more we believe it's possible for us to achieve it. That's why reward cards that say buy 12 get one free, with two purchases already 'given' to you are more effective than reward cards saying buy 10 get one free, with no purchases pre-stamped. Both cards require 10 purchases, but more people attain their free item and faster, with the card where they already had 2 stamps - simply because it appeared that they were already on their way. The goal seemed closer. Give yourself a perceived head start by designing goals with progress already achieved highlighted. Look backward to review how far you've come, which emphasizes the distance traveled rather than how far is yet to go.
3. Make it Bigger. This refers to the perceived likelihood of your achieving your goal. If we think that the possibility is small we create a visual in our minds of a very small target which implies that the odds of our ever hitting the target are also small, like the center of a bulls-eye. Instead, flip it. Make that Bulls-eye target larger than the rest of the board. Remind yourself of all of your past achievements, how well you have handled pressure, the difficulties you have overcome. Creating the expectation that this is just one more hurdle to jump in a long list of hurdles successfully overcome increases the psychological belief that you will also hit this target. It's now bigger.
4. Recalculate the Energy of Achievement. For every task we face our brain calculates out the perceived amount of energy and effort needed to achieve it. The more mental effort and energy required to accomplish a goal, the more likely we are to abandon it. To help maintain your focus then, it is important to avoid 'awfulizing' a task, making it seem like it will take an inordinate amount of time and effort. Stop watching the clock, tackle your more important tasks earlier in the day when your energy is higher, routinize your peripheral activities so they don't drain energy unnecessarily, don't tackle two challenging tasks back to back without building mental recovery time in between.
Fundamentally, the biggest key to achieving your goals faster is to train yourself to focus more of your brain's resources on success than on failure. Create your energy X-spots by focusing on your target and on how excellent your chances are of hitting it. Focusing your brain on how great your probability of success is will give you the energy and drive you need to succeed.