There are three principles to running fast: force production, speed off the ground, and strength. I think that when all of these principles line up, there will be an increase in speed. Disclaimer: there are also many more principles.
First, to get effective force production, there needs to be explosive strength and quickness. We establish this conditioning by doing specific types of lifts that increase the rate coding (how many muscle fibers that can fire). Here are a couple lifts that help with force production and overall strength.
1. Power Clean
This lift is an ultimate sprinters lift. It is a full body lift that focuses on the gluteus, hamstrings, and lower back. The two most important factors in this lift are the power output (the weight on the bar), and the speed of the bar. When one has a high power output and can move the bar at a maximal speed rate, there is an increase in one’s power. Overall, this lift is a transfer of power throughout the body that takes coordination, and synchronization. The power clean pushes from the heels, through the legs, to the core, and lastly the upper body action which is the clean.
2. Hang Clean
The Hang Clean is the second pull in the power clean. This is helpful with athletes who struggle in their second pull, and it is a little more difficult than the power clean. This is because, there is a tight window of space for the athlete to generate power, since the lift starts at the knees, or below the knees, in an athletic squat position. The hang clean eliminates upward movements and works to increase speed of the bar and force production in a tight window.
3. Deadlift
Of course Deadlift had to be on here! Deadlifting is essentially transferring over to how much force you can apply into the track when sprinting. There are two types of deadlifts, Romanian Deadlifts, and Trap Bar deadlifts. Personally, in sprinting, the trap bar deadlift is safer and more useful. In the trap bar deadlift, you are able to lift heavier, and thus reach certain weight numbers that will help you on the track with force production. The Romanian Deadlift focuses more on lower back development, hamstrings, and gluteus.