A : It is not possible to have constant velocity and variable acceleration.
R : Accelerated body cannot have constant velocity.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statement, then mark (4).

Answer

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

### Step 1: Understand the Assertion
The assertion states: "It is not possible to have constant velocity and variable acceleration."

- **Definition of Constant Velocity**: If an object has constant velocity, it means that its speed and direction are not changing over time. Mathematically, this implies that the change in velocity (Δv) is zero.

- **Definition of Variable Acceleration**: Variable acceleration means that the acceleration of the object is changing over time. This can be represented as different values of acceleration at different instances (a1, a2, a3, etc.).

### Step 2: Analyze the Relationship
- If the velocity is constant (Δv = 0), then the acceleration must also be zero (since acceleration is defined as the change in velocity over time, a = Δv/Δt).

- Therefore, if acceleration is variable, it implies that the velocity must be changing. Hence, it is impossible to have a scenario where the velocity remains constant while the acceleration varies.

### Conclusion for Assertion
The assertion is **correct** because constant velocity implies zero acceleration, and thus variable acceleration cannot coexist with constant velocity.

### Step 3: Understand the Reason
The reason states: "Accelerated body cannot have constant velocity."

- **Definition of an Accelerated Body**: An accelerated body is one that experiences a change in velocity over time. This means that its velocity is not constant.

- If a body is accelerating, it implies that there is a non-zero change in velocity (Δv ≠ 0). Therefore, the velocity of the body must be changing.

### Conclusion for Reason
The reason is also **correct** because an accelerated body, by definition, cannot maintain a constant velocity.

### Final Conclusion
Both the assertion and the reason are correct, and the reason correctly explains the assertion. Therefore, the answer to the question is that both statements are true, and the reason is a valid explanation for the assertion.

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