The net force acting on a body for one-dimensional motion is proportional to its rate of change of linear momentum. In this case, the linear momentum of the body is given by the equation p = a dt^2, where p is the linear momentum, a is a constant, and dt is the change in time.

The rate of change of linear momentum, dp/dt, can be found by differentiating the equation with respect to time.

Differentiating p = a dt^2 with respect to t, we get:

dp/dt = 2a dt

This shows that the rate of change of linear momentum, dp/dt, is directly proportional to 2a dt.

So, the net force acting on the body is proportional to 2a dt.

Explanation:
- Linear momentum: The linear momentum of an object is a vector quantity that represents the product of the object's mass and its velocity. It describes the amount of motion an object has in a straight line.
- Equation for linear momentum: The linear momentum of a body is given by the equation p = a dt^2, where p is the linear momentum, a is a constant, and dt is the change in time.
- Rate of change of linear momentum: The rate of change of linear momentum, dp/dt, represents how the momentum of an object changes with time. It can be found by differentiating the equation for linear momentum with respect to time.
- Proportional relationship: The equation dp/dt = 2a dt shows that the rate of change of linear momentum is directly proportional to 2a dt. This means that as the time interval dt increases, the rate of change of momentum also increases. Similarly, as the constant a increases, the rate of change of momentum increases.
- Net force and rate of change of momentum: According to Newton's second law of motion, the net force acting on an object is equal to the rate of change of its momentum. Therefore, the net force acting on the body is proportional to 2a dt, which represents the rate of change of linear momentum.

Right answer please?