Assertion : In the equation, `s=u+at-(1)/(2)a` where, s is the distance travelled by uniformly accelerated body in tth second.
Reason : The above equation is dimensionally incorrect.

Options

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

Answer

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

### Step 1: Understand the Assertion
The assertion states that in the equation \( s = u + at - \frac{1}{2}a \), where \( s \) is the distance traveled by a uniformly accelerated body in the \( t \)th second, the equation is correct.

### Step 2: Analyze the Equation
The equation can be rewritten for clarity:
\[ s = u + at - \frac{1}{2}a \]
This equation is intended to represent the distance traveled in the \( t \)th second. The term \( u \) represents the initial velocity, \( a \) represents acceleration, and \( t \) is the time.

### Step 3: Verify the Equation
To verify the assertion, we can derive the formula for the distance traveled in the \( t \)th second from the equations of motion. The distance traveled in the \( t \)th second can be expressed as:
\[ s_t = u + \frac{a}{2}(2t - 1) \]
When simplified, this gives:
\[ s_t = u + at - \frac{a}{2} \]
This matches the assertion, confirming that the assertion is correct.

### Step 4: Analyze the Reason
The reason states that the equation is dimensionally incorrect. We need to check the dimensions of both sides of the equation.

### Step 5: Check Dimensions
- The left-hand side (LHS) represents distance \( s \), which has the dimension of length:
\[ [s] = L \]

- The right-hand side (RHS) consists of three terms:
1. \( u \) (initial velocity) has dimensions of \( \frac{L}{T} \)
2. \( at \) (acceleration multiplied by time) has dimensions of \( L \) (since \( [a] = \frac{L}{T^2} \) and \( [t] = T \), thus \( [at] = \frac{L}{T^2} \times T = L \))
3. \( -\frac{1}{2}a \) (acceleration) also has dimensions of \( L \).

When we combine these terms:
- \( u + at - \frac{1}{2}a \) results in:
\[ \frac{L}{T} + L - L \]
This expression cannot be directly added because the first term has dimensions of \( \frac{L}{T} \), while the other two terms have dimensions of \( L \). Therefore, the dimensions do not match.

### Step 6: Conclusion
The assertion is correct, but the reason provided is incorrect because the equation is dimensionally incorrect. The reason does not explain the assertion correctly.

### Final Answer
The assertion is true, but the reason is false. Therefore, the correct option is that the assertion is correct, but the reason is not a valid explanation for the assertion.

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