A free body diagram of a object moving in air is suprisingly simple , only weight .Without air resistance the acceleration would be g downwards irrespective of whether it is moving in whatever direction.If air resistance is taken into account the resultant acceleration would depend on the direction of velocity as air resistance always oppose the motion.
For an object moving vertically upwards in the air encounter downwards force due to air resistance and hence its deceleration would be greater than g. Time taken to reach the highest point will be shorter than without air resistance.
For object moving vertically downwards would encounter an upwards force due to air resistance and hence its acceleration downwards would be less that g . Time taken to travel the same distance down would be less than without air resistance. Hence the time taken to rise up is less than the time taken to fall the same distance. Hence time up is less than time down .
