At the 'Car' select screen unlock the following cars using the gearstick.
Unlock Toyota Celsior: Highlight the Toyota Chaser and enter Neutral, 6, 4, 3.
Unlock Nissan Z31: Highlight the Nissan S30 and enter Neutral, 6, 4, 3.
Unlock Time Trial Mode: When you have inserted your coins the screen will prompt you to step on the Accelerator to start. Step on the Brake instead to enter Time Trial mode. Choose your car and step on the Accelerator to bring up the licensing screen to enter your initials. In Time Trial mode you are timed as you race to the checkpoints to earn extra time on the clock. There are no opponents challenging you in this mode.