Something like inheritance in database design

The type and id_in_type design is called Polymorphic Associations. This design breaks rules of normalization in multiple ways. If nothing else, it should be a red flag that you can't declare a real foreign key constraint, because the id_in_type may reference any of several tables.

Here's a better way of defining your tables:

• Make an abstract table Vehicles to provide an abstract reference point for all vehicle sub-types and vehicle tests.
• Each vehicle sub-type has a primary key that does not auto-increment, but instead references Vehicles.
• Each test sub-type has a primary key that does not auto-increment, but instead references Tests.
• Each test sub-type also has a foreign key to the corresponding vehicle sub-type.

Here's sample DDL:

CREATE TABLE Vehicles (
 vehicle_id INT AUTO_INCREMENT PRIMARY KEY
);

CREATE TABLE Speedboats (
 vehicle_id INT PRIMARY KEY,
 col_about_speedboats_but_not_tests1 INT,
 col_about_speedboats_but_not_tests2 INT,
 FOREIGN KEY(vehicle_id) REFERENCES Vehicles(vehicle_id)
);

CREATE TABLE Cars (
 vehicle_id INT PRIMARY KEY,
 col_about_cars_but_not_tests1 INT,
 col_about_cars_but_not_tests2 INT,
 FOREIGN KEY(vehicle_id) REFERENCES Vehicles(vehicle_id)
);

CREATE TABLE Gokarts (
 vehicle_id INT PRIMARY KEY,
 col_about_gokarts_but_not_tests1 INT,
 col_about_gokarts_but_not_tests2 INT,
 FOREIGN KEY(vehicle_id) REFERENCES Vehicles(vehicle_id)
);

CREATE TABLE Tests (
 test_id INT AUTO_INCREMENT PRIMARY KEY,
 col_about_all_tests1 INT,
 col_about_all_tests2 INT
);

CREATE TABLE SpeedboatTests (
 test_id INT PRIMARY KEY,
 vehicle_id INT NOT NULL,
 col_about_speedboat_tests1 INT,
 col_about_speedboat_tests2 INT,
 FOREIGN KEY(test_id) REFERENCES Tests(test_id),
 FOREIGN KEY(vehicle_id) REFERENCES Speedboats(vehicle_id)
);

CREATE TABLE CarTests (
 test_id INT PRIMARY KEY,
 vehicle_id INT NOT NULL,
 col_about_car_tests1 INT,
 col_about_car_tests2 INT,
 FOREIGN KEY(test_id) REFERENCES Tests(test_id),
 FOREIGN KEY(vehicle_id) REFERENCES Cars(vehicle_id)
);

CREATE TABLE GokartTests (
 test_id INT PRIMARY KEY,
 vehicle_id INT NOT NULL,
 col_about_gokart_tests1 INT,
 col_about_gokart_tests2 INT,
 FOREIGN KEY(test_id) REFERENCES Tests(test_id),
 FOREIGN KEY(vehicle_id) REFERENCES Gokarts(vehicle_id)
);

You could alternatively declare Tests.vehicle_id which references Vehicles.vehicle_id and get rid of the vehicle_id foreign keys in each test sub-type table, but that would permit anomalies, such as a speedboat test that references a gokart's id.