I’ll give you a sample warmup I use when I know I’m going to be doing a lot of dynamic stuff. For me this usually means a lot of jumping, but it would apply to sprinting.
Step 1- Raise Core Temperature
Usually for this I just jump rope for 3-5 minutes consecutively at a medium pace. The goal here is to raise your core temperature and get your heart rate up a bit.
Step 2- Dynamic Flexibility
Leg and Arm Swings
Step 3- Power Potentiation
Medicine Balls are a great tool to use for this. I like to do 20-30 total throws of medium intensity. I a few chest passes but mostly underhand tosses (using the legs), backwards keg-toss style or push-press throws. After this I do my last warmup exercise which is usually a maximal vertical jump. That might be a good idea for your, or just a few sub-maximal sprints as a final warmup.
A good warmup for strenuous dynamic effort should take 10-15 minutes to do properly, IMO. I’m not sure what level of a sprinter you are. The faster you are, the more taxing it is on your body and the more you will need to warmup to get a good effort and avoid injury.