Assertion : The displacement-time graph of a body moving with uniform acceleration is a straight line.
Reason : The displacement is proportional to time for uniformly accelerated motion.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false.
D. If the assertion and reason both are false

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that "The displacement-time graph of a body moving with uniform acceleration is a straight line."

- For a body moving with uniform acceleration, the displacement (s) is given by the equation:
\[ s = ut + \frac{1}{2} a t^2 \]
where \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.

- In this equation, the term \( \frac{1}{2} a t^2 \) indicates that displacement is not directly proportional to time; instead, it is proportional to the square of time. Therefore, the graph of displacement versus time will not be a straight line but a curve (specifically, a parabola).

**Conclusion for Assertion**: The assertion is **false**.

### Step 2: Analyze the Reason
The reason states that "The displacement is proportional to time for uniformly accelerated motion."

- From the equation of motion, we see that displacement is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
- The term \( ut \) is linear with respect to time, but the term \( \frac{1}{2} a t^2 \) shows that the overall displacement is not linear with respect to time; it is quadratic.

**Conclusion for Reason**: The reason is also **false**.

### Final Conclusion
Since both the assertion and the reason are false, the correct answer to the question is that both the assertion and the reason are false.

### Answer:
Both the assertion and the reason are false.

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