Why can't we travel at the speed of light?
The speed of light is the theoretical limit to the speed of an object. In fact, no object can reach the speed of light. Think about the scenario using Newton's Second Law of Motion which states that force is a product of mass and acceleration. For an object to be able to move with velocities comparable to that of light, some force has to be imparted to it. It has been found that an extraordinarily large amount of energy has to be spent to make something move with velocities comparable to that of light.
The Large Hadron Collider (LHC) in Switzerland is one of the most sophisticated machines ever built by human beings and even it has not been able to push electrons beyond 99.9999991% of the speed of light.
Another way to think of the impossibility of motion at or beyond the speed of light is that particles becomes extremely heavy as they approach the speed of light and hence the amount of energy required for their continued acceleration becomes impossibly large.
Hope this helps.