The correct option is (c).
Explanation
Average speed is a scalar physical quantity defined as the total path length travelled divided by the total time interval during which the motion has taken place. It represents the overall rate of motion for an object, regardless of variations in speed during the journey.
Statement-wise Analysis:
- Statement 1 is Correct: For an object undergoing uniformly accelerated motion (constant acceleration) in a straight line, the average speed (or average velocity magnitude) can be calculated as the arithmetic mean of the initial speed ($u$) and the final speed ($v$). The formula is given by $v_{avg} = \frac{u + v}{2}$.
- Statement 2 is Incorrect: Average speed is defined as the ratio of total distance to total time, not the product. It is calculated by dividing the total distance travelled by the total time taken ($v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}}$). Multiplying these quantities yields a dimensionally incorrect value ($L \times T$) for speed ($L/T$).
- Statement 3 is Correct: In non-uniform motion, the speed of an object changes over time. To describe the rate of motion for such an interval effectively, a single value called 'average speed' is used. It provides a standardized measure of how fast the object moved over the entire duration, smoothing out instantaneous fluctuations.
Key Takeaway:
Average Speed is the ratio of total distance to total time ($v_{avg} = \frac{s}{t}$). For uniformly accelerated rectilinear motion specifically, it can also be expressed as the mean of initial and final velocities ($\frac{u+v}{2}$).