While Tai Chi is often practiced slowly, when applied it is anything but slow. But to begin the slowness is beneficial to learning, correcting balance and slowly developing correct skills. However, if viewed with the open mind you can see its martial potential, from the initial push hand. Where you study pushing, pulling, pressing and warding off the attack, to DaLu the push hands when moving and cornering.
Then to the much more complex Opposing Person Form with a greater number of attacks with tai chi movements, and notice at each attack there is a corresponding tai chi counter for the attack.
Finally a look at Tai Chi potential at a faster speed.
Many programs no longer address the Tai Chi martial potential, but it is part of full training.