Assertion: Speed of a particle moving in a circle varies with time as, `u=(4t-12)` . Such type of circular motion is not possible.
Reason: Speed cannot change linearly with time.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, true but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and reason given in the question step by step.

### Step 1: Analyze the Assertion
The assertion states that the speed of a particle moving in a circle varies with time as \( u = 4t - 12 \). We need to determine if such a type of circular motion is possible.

1. **Understanding the Equation**: The equation \( u = 4t - 12 \) indicates that speed is a linear function of time. This means that as time increases, the speed will either increase or decrease linearly depending on the value of \( t \).
2. **Speed and Circular Motion**: In circular motion, the speed of the particle can change, but it must be accompanied by a centripetal force to maintain the circular path. If the speed decreases to zero (which happens when \( t < 3 \) in this case), the particle cannot continue in circular motion.

### Step 2: Analyze the Reason
The reason states that speed cannot change linearly with time.

1. **Understanding the Reason**: This statement is incorrect. Speed can indeed change linearly with time. For example, if an object is accelerating uniformly, its speed changes linearly with time.
2. **Conclusion about Reason**: Since speed can change linearly, this reason does not support the assertion.

### Step 3: Conclusion
- The assertion is **true** because a speed that decreases linearly can lead to a situation where the particle cannot maintain circular motion.
- The reason is **false** because speed can change linearly with time.

### Final Answer
The assertion is true, but the reason is false. Therefore, the correct option is that the assertion is true and the reason is false.

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