No, it is not possible for an object to have momentum without having kinetic energy. In classical mechanics, momentum and kinetic energy are directly related and are both properties associated with the motion of an object.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is expressed as:
p = m * v
where: p = momentum m = mass of the object v = velocity of the object
On the other hand, kinetic energy (KE) is the energy possessed by an object due to its motion. It is defined as one-half the product of the mass and the square of the velocity. Mathematically, kinetic energy is expressed as:
KE = (1/2) * m * v^2
As you can see, both momentum and kinetic energy depend on the mass and velocity of the object. If an object has momentum, it must be in motion, and if it is in motion, it possesses kinetic energy. These two quantities are interconnected and cannot be separated from each other.