A speed skater moving across frictionless ice at 9.0 m/s hits a 5.3 m -wide patch of rough ice. She slows steadily, then continues on at 5.8 m/s. What is her acceleration on the rough ice? Express your answer using two significant figures.
-0.302
To find the acceleration of the speed skater on the rough ice, we can use the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
Since the problem does not provide the time, we can use the equation for acceleration as it relates to distance:
acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)
Substituting the given values:
initial velocity = 9.0 m/s
final velocity = 5.8 m/s
distance = 5.3 m
acceleration = (5.8^2 - 9.0^2) / (2 * 5.3)
Simplifying this equation:
acceleration = (33.64 - 81) / 10.6
acceleration = -47.36 / 10.6
acceleration = -4.47 m/s^2
Therefore, the acceleration of the speed skater on the rough ice is approximately -4.47 m/s^2 (or -4.5 m/s^2 when rounded to two significant figures).
To find the acceleration on the rough ice, we can use the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
However, we do not have the time information in this question. Instead, we can use the kinematic equation that relates displacement, initial velocity, final velocity, and acceleration:
final velocity squared = initial velocity squared + 2 * acceleration * displacement
In this case, the initial velocity is 9.0 m/s, the final velocity is 5.8 m/s, and the displacement is the width of the patch of rough ice, which is 5.3 m. We can rearrange this equation to solve for acceleration:
acceleration = (final velocity squared - initial velocity squared) / (2 * displacement)
Now we can plug in the values to calculate the acceleration:
acceleration = (5.8^2 - 9.0^2) / (2 * 5.3)
acceleration = (33.64 - 81) / 10.6
acceleration = -47.36 / 10.6
acceleration ≈ -4.47 m/s^2 (rounded to two significant figures)
Therefore, the speed skater's acceleration on the rough ice is approximately -4.47 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
V^2 = Vo^2 + 2a*d.
V = 5.8 m/s.
Vo = 9.0 m/s.
d = 5.3 m.
Solve for a. It will be negative.