Yes, it is possible for an object to have momentum without having kinetic energy. Momentum and kinetic energy are two related but distinct concepts in physics.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, momentum is expressed as:
p = m * v
An object can have momentum as long as it has mass and is in motion or has a non-zero velocity. Even if the object is moving very slowly, it still possesses momentum, as long as its mass is non-zero.
On the other hand, kinetic energy (KE) is the energy an object possesses due to its motion. It depends not only on the object's mass and velocity but also on the square of its velocity. The formula for kinetic energy is:
KE = 0.5 * m * v^2
If an object is not moving (v = 0), its kinetic energy will be zero, even if it has mass and hence momentum.
In summary, an object can have momentum without kinetic energy if it has non-zero mass but is at rest or not moving (v = 0). However, if the object is in motion, it will have both momentum and kinetic energy.