Acceleration Calculation:
Acceleration can be calculated using the formula:
\[acceleration = \frac{change in velocity}{time taken}\]

Given Data:
Initial velocity, \(u = 2 m/s\)
Final velocity, \(v = 10 m/s\)
Time taken, \(t = 3 seconds\)

Calculating Change in Velocity:
Change in velocity, \(v - u = 10 m/s - 2 m/s = 8 m/s\)

Calculating Acceleration:
\[acceleration = \frac{change in velocity}{time taken} = \frac{8 m/s}{3 s} = 2.67 m/s^2\]
Therefore, the acceleration of the skater is \(2.67 m/s^2\).

Explanation:
When the skater increases her velocity from 2 m/s to 10 m/s in 3 seconds, she experiences an acceleration of 2.67 m/s^2. This acceleration represents the rate at which the skater's velocity is changing with respect to time. In this case, the skater is accelerating at a constant rate, resulting in a linear increase in velocity over the given time period.
Acceleration is a vector quantity, meaning it has both magnitude and direction. In this scenario, the skater's acceleration is in the direction of her velocity increase. As the skater continues to accelerate, her velocity will keep increasing until it reaches a constant value of 10 m/s.
Understanding the concept of acceleration is crucial in physics as it helps explain the motion of objects and the forces acting on them. In this case, the skater's acceleration of 2.67 m/s^2 indicates how quickly her velocity is changing and provides valuable insight into her motion.