ali, with whom allah is pleased, said:

‘you should have seen me on the day of badr! we sought refuge with the messenger of allah, may allah exalt his mention. he was the closest among of us to the enemy. on that day, the messenger of allah, may allah exalt his mention, was the strongest one among us.’  (ahmed #654)

as for his courage and bravery under normal circumstances - anas b. malik, with whom allah is pleased, said:

'the messenger of allah, may allah exalt his mention, was the best of people and the most courageous. one night, the people of madinah were frightened and headed towards the sounds they heard during the night. the messenger of allah, may allah exalt his mention, met them while coming back from the place of the sound, after he made sure that there was no trouble. he was riding a horse that belonged to abu talhah, with whom allah is pleased, without any saddle, and he had his sword with him. he was assuring the people, saying: 'do not be frightened! do not be frightened!’

anas, with whom allah is pleased, further said: ‘verily, we found the messenger of allah, may allah exalt his mention, to be like an ocean.’     (bukhari #2751)

he met up with people riding a horse with no saddle, and he carried his sword, for there might be a reason or need to use it. he did not wait for others to check out the source of trouble; as is done in these situations.

in the battle of uhud, the messenger of allah, may allah exalt his mention, consulted his companions. they advised him to fight, while he himself did not see the need to fight. however, he took their advice. the companions, upon learning the prophet’s feelings regretted what they had done. the ansaris said to him, 'o prophet of allah! do as you please.’ but, he replied:

‘it does not befit a prophet who has worn his war attire to remove it until he fights.'  (ahmed #14829)