STATEMENT-1 The kinetic energy gradient is proportional to acceleration of a particle moving along a straight line.
STATEMENT-2: Work done by net force is equal to increase in kinetic energy of a particle.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To analyze the given statements, we will break down each statement and provide a step-by-step solution.

### Step 1: Understanding Statement 1
**Statement 1:** The kinetic energy gradient is proportional to the acceleration of a particle moving along a straight line.

- **Kinetic Energy (KE)** of a particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the particle.

- The **gradient of kinetic energy** with respect to displacement \( x \) can be expressed as:
\[ \frac{d(KE)}{dx} = \frac{d}{dx} \left(\frac{1}{2} mv^2\right) \]

- To find the relationship between kinetic energy and acceleration, we can use the chain rule:
\[ \frac{d(KE)}{dx} = \frac{d(KE)}{dv} \cdot \frac{dv}{dx} \]
where \( \frac{dv}{dx} \) is the acceleration \( a \).

- Thus, we have:
\[ \frac{d(KE)}{dx} = mv \cdot a \]
This shows that the kinetic energy gradient is indeed proportional to acceleration.

**Conclusion for Statement 1:** True.

### Step 2: Understanding Statement 2
**Statement 2:** Work done by net force is equal to the increase in kinetic energy of a particle.

- This statement is a direct application of the **Work-Energy Theorem**, which states:
\[ W = \Delta KE \]
where \( W \) is the work done by the net force and \( \Delta KE \) is the change in kinetic energy.

- The work done by a force is calculated as:
\[ W = F \cdot d \]
where \( F \) is the net force and \( d \) is the displacement.

- According to the Work-Energy Theorem:
\[ W = KE_{final} - KE_{initial} \]
This confirms that the work done by the net force results in a change in kinetic energy.

**Conclusion for Statement 2:** True.

### Final Conclusion
Both statements are true. Statement 2 serves as a correct explanation for Statement 1 since it provides the foundational principle (Work-Energy Theorem) that supports the relationship stated in Statement 1.

### Answer Options
- **Option A:** Statement 1 is true, Statement 2 is true, and Statement 2 is a correct explanation for Statement 1. (This is the correct option.)