These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following five reponses
(a) If both Assertion and Reason arecorrect and Reason is the correct explanation of Asserrtion.
(b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
(c ) If Assertion is true but Reason is false.
(d) If Assertion is false but Reason is true.
Assertion Force applied on a block moving in one dimension is producing a constant power,then the motion should be uniformly accelerated.
Reason This constant power multiplied with time is equal to the change in kinetic energy.

Explanation

To solve the assertion and reason question, we will analyze both statements step by step.

### Step 1: Analyze the Assertion
**Assertion:** "Force applied on a block moving in one dimension is producing a constant power, then the motion should be uniformly accelerated."

- **Understanding Power:** Power (P) is defined as the rate at which work is done. If power is constant, it means that the work done over time is constant.
- **Work-Energy Principle:** The work done on an object is equal to the change in its kinetic energy. If the power is constant, the work done over a time interval can be expressed as:
\[ W = P \times t \]
- **Kinetic Energy:** The kinetic energy (K.E) of an object is given by:
\[ K.E = \frac{1}{2} m v^2 \]
- **Relationship Between Power and Kinetic Energy:** If we have constant power, the change in kinetic energy over time can be expressed as:
\[ \Delta K.E = P \times t \]
- **Acceleration Analysis:** If the kinetic energy is changing due to a constant power, we can derive the relationship between velocity and time. The velocity (v) can be expressed as:
\[ v \propto t^{1/2} \]
Differentiating this with respect to time gives us the acceleration (a):
\[ a = \frac{dv}{dt} \propto t^{-1/2} \]
This indicates that the acceleration is not constant, which means the motion is not uniformly accelerated.

### Conclusion for Assertion:
The assertion is **false** because constant power does not imply uniformly accelerated motion.

### Step 2: Analyze the Reason
**Reason:** "This constant power multiplied with time is equal to the change in kinetic energy."

- **Verification of Reason:** From our earlier analysis, we established that:
\[ W = P \times t = \Delta K.E \]
This is indeed true according to the work-energy theorem.

### Conclusion for Reason:
The reason is **true** as it correctly states the relationship between constant power and the change in kinetic energy.

### Final Answer:
Based on the analysis:
- Assertion is false.
- Reason is true.

Thus, the correct option is **(d) If Assertion is false but Reason is true.**

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