Stuff in space moves and will continue to move in the same direction at the same velocity until and if it comes in contact with another object or is subject to gravitational pull of some other object.
So, it’s exciting to have chases between ships, but real space has certain problems you must overcome in order for it to, well, be scientific. A ship is not “faster” than another ship. It can have greater acceleration and deceleration. However, once you are going faster than the ship you are chasing, you must decelerate when you’re in range with your weapons or you’ll see them for a bare second or two before you’re gone. Make that, decelerate before you reach them. A sudden burst of deceleration won’t work, especially if your rate of travel is up there in the thousands of miles per second. The math is uninteresting, but when you’re going really fast, you’ll need some way of slowing or changing your trajectory.
Therefore, a meeting engagement may be very brief, a few seconds, and then you may need a few months to turn around and come back to the fight. At high speed you turn slowly and it may take time to first slow to a stop, turn around, and accelerate to the point where you will overtake the ships you fought a few weeks ago.
Ultimately, it’s not how fast your ship is, it’s how much fuel you carry and how efficiently you can create thrust and whether that thrust or deceleration affects the people on the vessel. (I believe most authors make the mistake of assuming space ships are like airplanes or ocean going vessels in how they function. Nope. Not even close.