In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A: When a body moves on a curved path with increasing speed then angle between instantaneous velocity and acceleration is acute angle.
R: When the speed is increasing its tangential acceleration is in the direction of instaneous 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 statements then mark (4) .

Answer

To solve the given question, we need to analyze the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion
The assertion states that when a body moves on a curved path with increasing speed, the angle between the instantaneous velocity and acceleration is an acute angle.

### Step 2: Analyze the Conditions
When a body moves with increasing speed, it implies that the tangential acceleration (which is responsible for changing the speed) is in the same direction as the instantaneous velocity.

### Step 3: Use the Dot Product Concept
To determine the relationship between the acceleration and velocity, we can use the dot product:
\[ \mathbf{a} \cdot \mathbf{v} = |\mathbf{a}| |\mathbf{v}| \cos \theta \]
where \( \theta \) is the angle between the acceleration \( \mathbf{a} \) and the velocity \( \mathbf{v} \).

### Step 4: Establish the Condition for Increasing Speed
For the speed of the body to be increasing, the dot product \( \mathbf{a} \cdot \mathbf{v} \) must be positive:
\[ \mathbf{a} \cdot \mathbf{v} > 0 \]
This implies that:
\[ \cos \theta > 0 \]
Thus, \( \theta \) must be in the range where cosine is positive, which is between \( 0^\circ \) and \( 90^\circ \). Therefore, \( \theta \) is acute.

### Step 5: Understand the Reason
The reason states that when the speed is increasing, the tangential acceleration is in the direction of the instantaneous velocity. This is consistent with the assertion because if the tangential acceleration is in the same direction as the instantaneous velocity, it contributes positively to the speed of the body.

### Step 6: Conclusion
Since both the assertion and reason are correct, and the reason correctly explains the assertion, we conclude that both statements are true.

### Final Answer
Both the assertion (A) and the reason (R) are correct, and the reason is the correct explanation of the assertion.

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