Police Chase Down (PS2)

The english title for this one's a bit of a misnomer: though you do play as police officers, you aren't chasing anyone down, but are in fact on security detail. You pick one of four motorbike-riding police officers (amusingly, three of them get descriptions like "member of an elite unit" or "the force's most decorated officer", while one guy is just "a respected highway patrol officer"),and go on missions to protect limosines

from gangs of thugs on motorbikes and in vans, who would cause harm to the passengers within. So it's like Chase HQ, minus the chase, but plus escort missions.
Having to protect a fairly slow-moving vehicle while riding a quite fast one is really fiddly, and you'll often be either turning round to go back and fight enemies who've appeared from the rear, or just plodding along as slow as you can (which means pressing the accelerator every few seconds, since the game doesn't support the Dual Shock 2's analogue buttons) to keep pace with the limo.
If the limo's health is reduced to zero, or the time runs out, you fail the mission, if the limo reaches its destination, you succeed. But while you're playing, the game doesn't actually tell you how far you are from the goal, which is annoying, and leaves the player in a kind of limbo, not knowing whether or not the limo has

enough health left to make it. Which it might not anyway, as it might drive into some obstacle you didn't see and instantly lose all its health, which happened to me once.
I could go as far as to say that Police Chase Down is the second-worst of the PS2 Simple Series games I've played, with only Eternal Quest/The Dungeon RPG being worse on account of the fact that it's incredibly boring and the PAL version isn't even fully translated!
So in summary, I don't recommend this or Eternal Quest.
This game is also known as The Simple 2000 Ultimate Series Vol. 7: Saikyou! Shirobi King ~Security Police~