To determine which statements regarding work are true, we can analyze each statement based on the principles of work, energy, and power in physics.
### Step-by-Step Solution:
1. **Understanding Work and Kinetic Energy:**
- Work done by a force on an object is related to the change in kinetic energy of that object. According to the work-energy theorem, the work done (W) by a net force acting on an object is equal to the change in its kinetic energy (ΔKE).
- Mathematically, this is expressed as:
\[
W = \Delta KE = KE_f - KE_i
\]
- Where \( KE_f \) is the final kinetic energy and \( KE_i \) is the initial kinetic energy.
2. **Analyzing Statement A:**
- **Statement:** "The force does positive work on a body if its kinetic energy is increasing."
- If the kinetic energy is increasing, it implies that work done by the net force is positive. Hence, this statement is **true**.
3. **Analyzing Statement B:**
- **Statement:** "A force can do zero work even if the kinetic energy is changing."
- This can occur if there are multiple forces acting on the object. For example, if one force does positive work and another does equal negative work, the net work can be zero while the kinetic energy changes due to the other forces. Thus, this statement is **true**.
4. **Analyzing Statement C:**
- **Statement:** "A force can do negative work even if the kinetic energy of the body is increasing."
- This is possible if the negative work done by one force is outweighed by the positive work done by other forces. For instance, friction can do negative work while another force accelerates the object. Therefore, this statement is **true**.
5. **Analyzing Statement D:**
- **Statement:** "A force does positive work if the angle between the force vector and displacement vector is acute."
- The work done by a force is given by the dot product of the force and displacement vectors, which involves the cosine of the angle between them:
\[
W = F \cdot S = F S \cos(\theta)
\]
- If the angle \( \theta \) is acute (less than 90 degrees), then \( \cos(\theta) \) is positive, leading to positive work. Hence, this statement is **true**.
### Conclusion:
All the statements A, B, C, and D are true regarding work.
