There can be only subjective answers to your question. There is no "lowest," since it depends on how you define "significant," but 0.5c is usually considered to be the point were the rate of change begins to take off rapidly.
bandwidth
Any fraction that you like.
5mph
5 strokes
water.
In the film 'Interstellar', the spacecraft called Endurance travels at a significant fraction of the speed of light, specifically around 90% of the speed of light, which is approximately 270,000 kilometers per second.
0 MPH
cali
21/25
A complete stop.
Solids.
1/500