A speed skater moving across frictionless ice at 8.0 m/s hits a 5.7m-wide patch of rough ice. She slows steadily, then continues on at 6.5m/s.
What is her acceleration on the rough ice?
5.7 = 8t + 1/2 at^2
6.5 = 8 + at
a = -1.9079 m/s^2
t = 0.7862 s
To calculate the acceleration of the speed skater on the rough ice, we can use the formula:
acceleration = (final velocity - initial velocity) / time
However, the time is not given directly in the problem. But we can determine the time by using the distance and the average velocity.
The skater moves from 8.0 m/s to 6.5 m/s, covering a distance of 5.7 m. Since the acceleration is constant, the average velocity can be used to find the time taken to traverse the rough ice.
average velocity = (initial velocity + final velocity) / 2
Let's calculate the average velocity first:
average velocity = (8.0 m/s + 6.5 m/s) / 2 = 7.25 m/s
Now, we can calculate the time:
time = distance / average velocity = 5.7 m / 7.25 m/s ≈ 0.79 s
Now, we can substitute the values into the acceleration formula:
acceleration = (final velocity - initial velocity) / time
= (6.5 m/s - 8.0 m/s) / 0.79 s
= -1.90 m/s²
Therefore, the speed skater's acceleration on the rough ice is approximately -1.90 m/s². The negative sign indicates that the acceleration is in the opposite direction of motion.