I know the acceleration due to gravity (ie 9.8 m/s2) will have a negative sign when falling down, a positive one when going up. My question is, will the acceleration due to gravity always have a positive sign when the object is moving faster, and will the acceleration due to gravity always have a negative sign when an object slows down

Yes

Explanation:

Accerelation is measured by change in velocity. So naturally, if an object is slowing down, its velocity is decreasing so acceleration is negative. If it is speeding up velocity is increasing so positive acceleration.

(Velocity final - Velocity initial)/t

Note that this does not apply only to gravity, but to all linear accelerations

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

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