The linear momentum P of a body varies with time and is given by the equation P=x+yt2, where x and y are constants. The net force acting on the body for a one dimensional motion is proportional to-

Options

A. (a)`t^(2)`
B. (b)`t^(o)`
C. (c)`t^(-1)`
D. (d)t

Answer

To solve the problem, we need to analyze the given equation for linear momentum and derive the expression for the net force acting on the body.

### Step-by-Step Solution:

1. **Identify the given equation for momentum**:
The momentum \( P \) of the body is given by the equation:
\[ P = x + yt^2 \]
where \( x \) and \( y \) are constants.

2. **Recall the relationship between force and momentum**:
The net force \( F \) acting on an object is defined as the rate of change of momentum with respect to time:
\[ F = \frac{dP}{dt} \]

3. **Differentiate the momentum equation with respect to time**:
We will differentiate \( P \) with respect to \( t \):
\[ \frac{dP}{dt} = \frac{d}{dt}(x + yt^2) \]
Since \( x \) is a constant, its derivative is zero. The derivative of \( yt^2 \) with respect to \( t \) is:
\[ \frac{d}{dt}(yt^2) = 2yt \]
Therefore, we have:
\[ F = \frac{dP}{dt} = 0 + 2yt = 2yt \]

4. **Identify the proportional relationship**:
From the expression \( F = 2yt \), we can see that the force \( F \) is directly proportional to \( t \) (since \( 2y \) is a constant):
\[ F \propto t \]

5. **Conclusion**:
The net force acting on the body for one-dimensional motion is proportional to \( t \).

### Final Answer:
The net force acting on the body for one-dimensional motion is proportional to \( t \).