Bullet time until relativity applies, at which point everybody dies.
It's a matter of how fast he goes, for as long as speed remain within the bounds for normal Newtonian movement you get the Matrix bullet time effect, everyone else looks slow. However if he keeps accelerating to relativistic speeds he hits the xkcd relativistic baseball threshold slightly ahead of significant time dilation.
The ball is going so fast that everything else is practically stationary. Even the molecules in the air are stationary. Air molecules vibrate back and forth at a few hundred miles per hour, but the ball is moving through them at 600 million miles per hour. This means that as far as the ball is concerned, they’re just hanging there, frozen.
The ideas of aerodynamics don’t apply here. Normally, air would flow around anything moving through it. But the air molecules in front of this ball don’t have time to be jostled out of the way. The ball smacks into them so hard that the atoms in the air molecules actually fuse with the atoms in the ball’s surface. Each collision releases a burst of gamma rays and scattered particles.
These gamma rays and debris expand outward in a bubble centered on the pitcher’s mound. They start to tear apart the molecules in the air, ripping the electrons from the nuclei and turning the air in the stadium into an expanding bubble of incandescent plasma. The wall of this bubble approaches the batter at about the speed of light—only slightly ahead of the ball itself.
You get the general idea.
Everybody's dead, Dave
Better to slow down a little.