A speed skater moving to the left across frictionless ice at 8.6 m/s hits a 4.7-m-wide patch of rough ice. She slows steadily, then continues on at 5.3 m/s. What is her acceleration on the rough ice?

 a = 4.88 m / s²

Explanation:

We can solve this exercise using the expressions of kinematics in one dimension

         v² = v₀² - 2a x

where v is the velocity, v₀ is the initial velocity, at acceleration and ax is the distance, the negative sign is because the velocity decreases because

          a = (v₀² - v²) / 2x

let's calculate

         a = (8.6² - 5.3²) / (2   4.7)

         a = 4.88 m / s²