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That force is proportional to the velocity with which it is moving. This yes, the drag force or viscous force will increase as the velocity increases and this is generally associated with the object moving in fluids like water or air(freely falling).
Think of an object moving over ice or something flying through space. There's little or no friction and the object continues at its speed. But when you are flying down the road on a bicycle and you put your feet flat on the ground to slow down...the friction of the sole of your shoe drags across the road and slows you down. Friction decreases speed.
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