According to Einstein's theory of special relativity, as an object with mass approaches the speed of light, its mass increases, and time dilation occurs. However, the experience of the observer traveling at near the speed of light is subjective. From the perspective of the observer, they would not perceive any difference in their own speed.
This is due to the concept of relativity, where the observer's perception of motion is always relative to their frame of reference. When you are in a moving vehicle, such as a car or an airplane, you do not feel the motion because you are moving with the same velocity as the vehicle. Similarly, if you were traveling close to the speed of light, your frame of reference would be moving along with you, and you would not feel any change in speed.
However, from the perspective of an outside observer, there would be observable effects. For example, time would appear to be passing more slowly for the object moving at high speeds compared to the stationary observer. Additionally, the object's length would appear to contract in the direction of motion. These phenomena are consequences of time dilation and length contraction predicted by special relativity.
In summary, the lack of perceived difference in speed when traveling close to the speed of light is due to the observer's frame of reference moving along with them.