Statement I: The average velocity of the body may be equal to its instantaneous velocity.
Statement II: For a given time interval of a given motion, average veocity is single valued while average speed can have many values.

Options

A. Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I.
B. Statemnt I is true, Statement II is true, Statement II is true, Statement II is false.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.

Explanation

To solve the question, we need to analyze both statements provided.

### Step 1: Understand Average Velocity
Average velocity is defined as the total displacement divided by the total time taken. Mathematically, it can be expressed as:
\[ \text{Average Velocity} = \frac{\Delta x}{\Delta t} \]
where \(\Delta x\) is the total displacement and \(\Delta t\) is the total time.

### Step 2: Understand Instantaneous Velocity
Instantaneous velocity is the velocity of an object at a specific moment in time. It can be found by taking the derivative of the displacement with respect to time or by finding the slope of the tangent to the displacement-time graph at that point.

### Step 3: Analyze Statement I
Statement I claims that the average velocity of the body may be equal to its instantaneous velocity. This is true in certain conditions, for example, when the motion is uniform (constant velocity) or when the time interval considered is infinitesimally small. Therefore, Statement I is **correct**.

### Step 4: Analyze Statement II
Statement II states that for a given time interval of a given motion, the average velocity is single-valued while the average speed can have many values. This statement is misleading. Average velocity is indeed single-valued for a given time interval as it is defined based on total displacement. However, average speed, which is the total distance traveled divided by the total time, can also be a single value for that time interval. Therefore, Statement II is **incorrect**.

### Conclusion
- Statement I is **correct**.
- Statement II is **incorrect**.

Thus, the correct option is that Statement I is true and Statement II is false.

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