acceleration?

how can i make an object accelerate slowly in the game engine?

Using servo motion.

Use a physics with dynamic objects

F = Force
m = mass of object
a = acceleration

F = m * a >>> a = F / m.

Less Force or more mass will cause slower acceleration.

There’s a ‘Damp’ value setting in Logic menu (F4-key) to give a simplified aerodynamic drag characteristic for your object to prevent a ‘Ludicrous speed’ as a result of never ending acceleration.