The more explosive strength you have in relation to your bodyweight, the quicker and more agile you tend to be. Some of those lean, 170lb ripped-to-the-bone powerlifters are like quicksilver... they may not look strong or fast, but believe me, those guys are the closest thing there is to men of steel (maybe a misleading comparison since steel = heavy, rigid... ah well, that's the best I could come up with).
Anyways, if you want speed and strength, try to focus on basic, heavy movements- primarily (squat, bench, deadlift etc), and get your bodyfat down.
For sprinting i would highly recommend playing Squash. Once you learn the game and get halfway decent you will find yourself using bursts of speed over small distances, turning, bursting somewhere else, turning, sprinting across the court etc etc. A few weeks of this and you will see an improvement for sure.
Everyone on this board is right, squats, bench, deadlifts are all good for strength. but they are slow motion lifts. You need cleans(explosion), box squat(heavier but a fast movement, snatch squats(balance) and sometimes high reps for endurance. Also it sounds stupid but moving your foot back and forth for a minute on minute off is good to cause the whole point of running fast is to move your feet off the ground as fast as you can.
I am a state champion with a former 40 time of 4.42(fat) 4.2 handheld. Also hip flexors are great along with a strong stomach(form is everything). Also cross training with boxing is great because You can only move as fast as your arms will let you.
Also depending on what you are trying to achieve(distance) if you want a faster 40 time run 45 meters 100(110,120) 200 (220,240) and so on. And dont over work yourself. you do that you gain nothing. If you need to know anything more let me know I have much expoerience with track and football.
I used to do sprints in Strength Shoes back when I used to play basketball and shit. My speed increased a lot and Vertical about 6". That was about 5-6 years ago. Now I am a lot slower and my vertical dropped by 8" easy.
It depends what kind of quicker. If you want bursts of speed and explosion then go for lots of sqats and calf workouts with lots of weight. Like where you could barely do 5 reps of squats and 20-30 reps of high weight calf raises. This is great for the 100 and 200, especially your 40s. If you want to get better at something like your 400, possibly 800 if you are in great shape and can keep up the running you want to do squats and calfs but do lower weights but do them extremely fast and lots of them. Like 20 or more squats very quickly and a lot of calf raises. Low reps and high weight will make you a lot stronger and give lots more mass as well as those bursts or explosions. With lower weight and lots of reps it tones better and makes your muscles all around faster. your reflexes will be faster and you will be more springy. Good for hurdles and sprinting for longer periods.