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

### Step-by-Step Solution:

**Step 1: Understand the Assertion (A)**
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 Motion**
When a body moves along a curved path, it experiences two types of acceleration:
- **Tangential Acceleration (At)**: This is responsible for the change in the speed of the body. Since the speed is increasing, At is directed in the same direction as the instantaneous velocity.
- **Centripetal Acceleration (Ac)**: This is responsible for the change in direction of the velocity and is directed towards the center of the curvature of the path, which is perpendicular to the instantaneous velocity.

**Step 3: Determine the Angle Between Velocity and Acceleration**
Since At is in the direction of the instantaneous velocity and Ac is perpendicular to it, the net acceleration (A_net) can be represented as the vector sum of At and Ac. The angle (θ) between the instantaneous velocity (v) and the net acceleration (A_net) can be determined using vector addition.

- The angle θ formed between the instantaneous velocity and the resultant acceleration (A_net) will always be less than 90 degrees (π/2 radians) because At is in the same direction as v, and Ac is perpendicular to v.

**Step 4: Conclusion on Assertion**
Since θ < 90 degrees, we conclude that the assertion is true; the angle between instantaneous velocity and acceleration is indeed an acute angle.

**Step 5: Understand the Reason (R)**
The reason states that when the speed is increasing, the tangential acceleration is in the direction of the instantaneous velocity.

**Step 6: Validate the Reason**
As the speed of the body increases, tangential acceleration (At) must act in the same direction as the instantaneous velocity to increase the speed. This is consistent with the definition of tangential acceleration, which is responsible for changes in the magnitude of velocity (speed).

**Step 7: Conclusion on Reason**
Since the reason correctly explains why the angle between instantaneous velocity and acceleration is acute (because At is aligned with v), the reason is also true.

### Final Conclusion:
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

### Answer:
Both assertion and reason are true, and the reason is the correct explanation of the assertion.