I decelerate the velocity of my robot very quickly by applying a common voltage (eg. 24V to both the terminals using Motor driver) to the DC motors. Given, the motor is running at a very high speed and suddenly a common voltage of 24V is applied to the motors. I suppose the kinetic energy should dissipate in the armature resistance. Is it safe for the motors or external braking is advisable?
You can do various Bad Things to a motor by doing this -- but whether it's bad for your motor in your machine depends on what you're doing.
When you short a motor like that, it'll generate a lot of current, and in addition to heating up the armature, that current can damage the commutator or brushes. On older motors it could demagnetize the magnets, but that's probably not an issue if your motor has rare-earth magnets.
You can compute the current from the motor's speed, it's speed vs. voltage constant and its armature resistance. Compare that to the motor datasheet's maximum current. A good motor datasheet will have not only a maximum current, but some sort of instantaneous current that gives you an idea of how much of an overload you can give it for how long.
You may also want to consider how much torque the motor will be absorbing during this, and ask whether you'll be exceeding your mechanism's strengths. You'll know the current, so use the motor's torque vs. current constant to calculate the torque, and compare that to the capability of whatever you have the motor attached to.