There are definitely mental aspects to performance. Willpower, which gives us the ability to do things that are difficult, is key aspect of physical performance. Until recently, it was thought to be a limited resource – in other words, it could be ‘used up’ or reduced if you used it a lot. However this has been called into question.
Recent research has found that swearing can reduce pain, so cyclists, for example, can keep going through the pain if they repeat a swear-word over and over again! The theory behind this is that swearing activates the physiological experience of stress (‘fight or flight’) by increasing heart rate and arousing the autonomic nervous system. This puts us into a state where we can tolerate higher levels of pain.
Therefore, the brain, mental processes and the body can be thought of as one dynamic system, and performance can be considered to have both mental and physical aspects. There will always be physical limitations, however: if you didn’t have strong enough arm muscles you probably couldn’t life a car no matter how much you wanted to (and no matter how many swear words you used!!)
Rose has already covered this pretty well, but I think in some situations it can be down to the adrenaline caused by the situation – like in the situation you describe! This is why sometimes people can get sudden bursts of ‘superhuman strength’ that just seem to come out of nowhere!