A point moves along an arc of a circle of radius `R`. Its velocity depends on the distance `s` covered as `v=lambdasqrt(s)`, where `lambda` is a constant. Find the angle `theta` between the acceleration and velocity as a function of `s`.

Explanation

To solve the problem, we need to find the angle \( \theta \) between the acceleration and the velocity of a point moving along an arc of a circle with a given velocity function. The velocity \( v \) is defined as \( v = \lambda \sqrt{s} \), where \( \lambda \) is a constant and \( s \) is the distance covered.

### Step-by-Step Solution:

1. **Identify the Components of Acceleration**:
- The total acceleration \( \vec{a} \) of the point can be broken down into two components:
- **Tangential Acceleration** (\( a_t \)): This is due to the change in speed along the path.
- **Centripetal Acceleration** (\( a_c \)): This is due to the change in direction of the velocity as the point moves along the circular path.
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