A speed skater moving across frictionless ice at 9.0 hits a 6.0 -wide patch of rough ice. She slows steadily, then continues on at 6.1 m/s. What is her acceleration on the rough ice?
a = ∆(v^2)/2s = (6.1^2 - 9^2)/12 = -3.65
To find the acceleration of the speed skater on the rough ice, we need to use the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 9.0 m/s and the final velocity is 6.1 m/s. We are not given the time it takes for the speed skater to slow down, but since the question states that she slows steadily, we can assume that the time is the same for both accelerations.
If we subtract the initial velocity from the final velocity, we get:
6.1 m/s - 9.0 m/s = -2.9 m/s
The negative sign indicates that the speed skater is slowing down. Now we need to divide this change in velocity by the time it takes for her to slow down. Since we don't have the value for time, we can't calculate the acceleration directly.
If you have additional information or equations related to the time it takes for the speed skater to slow down, you can use that to find the acceleration. Otherwise, without the value of time, we can't determine the exact acceleration on the rough ice.