Hey! Bottom line, up front: check your starter, starter solenoid or alternator. Any auto parts store will check to see if they are the culprit when you take them off (all are <30 minute jobs).
I had the same issue on my 87 f150 (5.0 V-8) when I bought it. I would turn it over and it would lag on the start (didn't feel complete). I didn't worry until this weekend when the alternator would not stop when I attempted to turn off the engine. I noticed a funny smell and thought alternator. After changing that, then the starter solenoid, I lastly changed the starter and viola, solid complete feeling start. Hope this helps.