To unlock the Speed Makes You Cleverer trophy in The Grand Tour Game, you will need to use the More Horsepower powerup 50 times. You collect the pickups by driving into one of the balloons that appear in races. Which powerup you get is random. You can speed this up by doing them all in one race without the need of a second controller or racing against AI.
From the main menu go to Local Splitscreen > Face Off
In the race settings, choose the following:
Car Class: Any
Track Selection: Choose
AI Vehicle Class: AI Off
Season 1 - Episode 1
Rabbit Dry Lake
Once you start the race, drive to the first set of balloons and position your car so that you can drive forwards and backwards across the ballons repeatedly.
You can only have two powerups stored at once, so just keep popping the balloons and pressing the X button to activate them. Unfortunately, the trophy will only pop once the race has been completed and your stats to update. Probably takes about 10-15 minutes of this method to unlock all of the powerup trophies from the base game in the one race.