Acceleration and speed are related to force-to-weight and power-to-weight ratios.
The amount of force you can put down on the field is your weight multiplied by the coefficient of friction between your feet and the ground. If you have a coefficient of friction of 1.5, this means you can exert 150 lbs of accelerative force for every 100 lbs you weigh.
F=m*a, so a = F/m. If I can put down 300 lbs of accelerative force, and I weigh 150 lbs, I can accelerate at 2g, or 25 yards per second, per second. This allows me to reach my 11 yard per second top speed in 44/100 of a second, during which I’ll have covered 2 1/2 yards. If I can only put down 100 lbs of force, I can only accelerate at 2/3g, or 8 meters per second per second. It’ll take me 1.37 seconds to reach top speed, and this’ll take up 8 yards.
Now, for a real-world example, let’s take two players. “Chuck” is a 150-lb running back with a maximum accelerative force of 375 lbs. “Tony” is a 250-lb linebacker who can exert a maximum accelerative force of 400 lbs. Chuck stops accelerating at 11 yards per second (seriously fast - Michael Bennett or Clinton Portis-fast). Tony stops accelerating at 10 yards per second (seriously fast for a linebacker).
The play is the old Green Bay power sweep - race 20 yards across the field from the left hashmarks to a couple yards from the sideline, then turn upfield. If it works anywhere near right, all the tacklers aside from the left linebacker are blocked by the linemen and fullback. The running back and left linebacker line up roughly equidistant from a point twenty yards across to the right and five yards upfield of the running back.
The first time we look at this play, it’s in the RCA dome in Indianapolis. Between the rubberized plastic “grass” and the rubber soles of the players’ shoes, the coefficient of friction is 2.5. Chuck and Tony line up on opposite sides of the ball. The ball is snapped and the drag race begins.
Chuck accelerates to 11 yards/second at 2.5g, reaching it in .41 seconds and 2.25 yards. He covers the other 17.75 yards at full speed and reaches it 1.61 seconds later, 2.02 seconds after the snap.
Tony accelerates to 10 yards/second at 1.6g, reaching it in .58 seconds and 2.9 yards later. He covers the other 17.1 yards in 1.71 seconds, for a total of 2.3 seconds after the snap.
He is three tenths of a second, or three yards, behind Chuck. If the receivers can throw half-decent blocks on the DBs, this is “six points and a try”.
Now, let’s try it on a slick, muddy field in Gillette. Despite cleats that would qualify as torture instruments under the Geneva convention, the coefficient of friction is down to .85. Same play - let’s go.
Chuck could accelerate at 2.5 g - if he could put down 375 lbs of force. He can’t. He weighs 150 lbs - and can put down a measly 123 lbs of force. Moreover, he’s got to modulate this force - if he tries to overdo it, he’ll slip and skid. He cuts back to 110 lbs of force.
Tony could accelerate at 1.6g - if he could put down 400 lbs of force. He can’t, either - but he can put down about 200 lbs.
The ball is snapped.
Chuck accelerates at 7 yards per second per second, reaching his top speed in 1.57 seconds, 8.6 yards later. He then takes 1.02 seconds to reach the turning point, for a total of 2.60 seconds to reach the turning point.
Tony accelerates at 7 yards per second per second, reaching his top speed in 1.42 seconds, 7.1 yards later. He takes 1.3 seconds to reach the point, for a total of 2.7 seconds. 1/10 of a second is 1 yard. He can tackle Chuck right there if he can dive at all.