Which of the following should be constant for a body to have a constant momentum?

The correct option is "All of the above".

To understand why all of the given physical quantities must be constant for a body to have a constant momentum, let us break down the physical concepts step-by-step:

1. Momentum and Velocity:
The linear momentum ($p$) of a body is defined as the product of its mass ($m$) and its velocity ($v$):

$p=m·v$

For a body of constant mass ($m$), the momentum is directly proportional to its velocity. Therefore, for the momentum to remain constant, the Velocity of the body must remain constant.

2. Acceleration:
Acceleration ($a$) is defined as the rate of change of velocity with respect to time:

$a=\frac{dv}{dt}$

If the velocity ($v$) is constant, its rate of change over time is zero. Thus, the acceleration must be constantly zero ($a=0$). A constant value of zero is still a constant. Therefore, Acceleration must be constant (specifically, zero).

3. Force:
According to Newton's second law of motion, the net external force ($F$) acting on a body is equal to the rate of change of its momentum:

$F=\frac{dp}{dt}$

If the momentum ($p$) is constant, its derivative with respect to time is zero. This means the net external force acting on the body must be constantly zero ($F=0$). Since zero is a constant value, the net Force must also be constant.

Conclusion:
For a body to maintain a constant momentum, its velocity must be constant, which mathematically requires both its acceleration and the net external force acting on it to be constantly zero. Thus, velocity, acceleration, and force must all remain constant.