The total work done on a particle is equal to the change in its kinetic energy

Options

A. always
B. only if the forces acting on the body are conservative
C. only in the inertial force frame
D. only if no external force is acting

Answer

To solve the question, "The total work done on a particle is equal to the change in its kinetic energy," we can follow these steps:

### Step 1: Understand the Work-Energy Theorem
The Work-Energy Theorem states that the total work done on a particle is equal to the change in its kinetic energy. Mathematically, this can be expressed as:
\[ W = \Delta KE \]
where \( W \) is the work done, and \( \Delta KE \) is the change in kinetic energy.

### Step 2: Define 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.

### Step 3: Analyze the Change in Kinetic Energy
The change in kinetic energy when a particle goes from an initial velocity \( v_i \) to a final velocity \( v_f \) can be calculated as:
\[ \Delta KE = KE_f - KE_i = \frac{1}{2} mv_f^2 - \frac{1}{2} mv_i^2 \]

### Step 4: Apply the Work-Energy Theorem
According to the Work-Energy Theorem, the total work done on the particle (which can include both conservative and non-conservative forces) results in the change in kinetic energy:
\[ W = \Delta KE \]
This holds true regardless of the type of forces acting on the particle.

### Step 5: Conclusion
From the analysis, we conclude that the statement "The total work done on a particle is equal to the change in its kinetic energy" is true in all scenarios, provided we consider all forces acting on the particle. Therefore, the correct answer to the question is:
**Always.**