First time doing sprints.. How do I make my legs stronger?

Im not a competitive athlete, but I took up sprinting for health reasons and to stay in good cardiovascular shape.

I sprint for about 10 seconds full speed in the parking lot and about 5 seconds in... my power is just gone. Its like ive completely lost all acceleration and its as if im "bouncing off the rev limiter" just to finish the sprint.

Are there any good leg exercises you guys recommend to help me be able to power through the last few seconds? Thanks.