Kinetic energy of a particle is found to increase continuously with time . Select correct statement (s) .

Options

A. Resultant force acting on the particle must always be at angle less than `90^(@)` with the velocity of particle .
B. Resultant force may always bee parallel to velocity of the particle .
C. Magnitude of linear momentum of the aprticle increases with time .
D. Resultant force must always be parallel to velocity of the particle .

Explanation

To solve the problem regarding the kinetic energy of a particle increasing continuously with time, we will analyze the implications of this statement step by step.

### Step 1: Understanding Kinetic Energy
Kinetic energy (KE) of a particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its velocity. If the kinetic energy is increasing with time, it implies that the velocity of the particle must also be increasing.

**Hint:** Remember that kinetic energy depends on the square of the velocity.

### Step 2: Analyzing Change in Kinetic Energy
The change in kinetic energy can be expressed as:
\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
If \( \Delta KE \) is positive, it indicates that the kinetic energy is increasing. This can occur if the velocity of the particle is increasing.

**Hint:** Consider how changes in velocity affect kinetic energy.

### Step 3: Applying the Work-Energy Theorem
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy:
\[ W = \Delta KE \]
If the kinetic energy is increasing, then the work done by the net forces acting on the particle must also be positive.

**Hint:** Work done is related to the forces acting on the particle.

### Step 4: Understanding Force and Work
The work done can be expressed as:
\[ W = F \cdot d = F \cdot ds \cos \theta \]
where \( F \) is the net force, \( d \) is the displacement, and \( \theta \) is the angle between the force and the displacement. For work to be positive, \( \theta \) must be between \( 0^\circ \) and \( 90^\circ \).

**Hint:** Think about the direction of the force relative to the motion of the particle.

### Step 5: Evaluating the Statements
1. **Statement A:** Resultant force must act on the particle at an angle less than \( 90^\circ \) to the velocity. This is correct because a positive work implies that the force has a component in the direction of the displacement.

2. **Statement B:** The resultant force may be parallel to the velocity of the particle. This is also correct, as a parallel force would maximize the increase in kinetic energy.

3. **Statement C:** The magnitude of linear momentum is increasing. Since momentum \( p = mv \), if the velocity is increasing, the momentum must also increase, hence this statement is correct.

4. **Statement D:** Resultant force must always be parallel to the velocity. This is incorrect because the force does not have to be parallel to increase kinetic energy; it just needs to have a positive component in the direction of motion.

### Conclusion
The correct statements regarding the scenario where the kinetic energy of a particle increases continuously with time are A, B, and C.

**Final Answer:** The correct statements are A, B, and C.