Understanding Acceleration: How a Speed Skater Slows Down on Rough Ice

[vbplaya]

Acceleration.. Need Help !

A speed skater moving across frictionless ice at 8 m/s hits a 5 m wide patch of rough ice. She slows steadily, then continues on at 6m/s. What is her acceleration on the rough ice?

Please help. I don't know how to solve this.

 

[vbplaya]

nevermind. i figured it out.

 

[quicknote]

Acceleration is the rate of change of an object's velocity over time. In this scenario, the speed skater's initial velocity is 8 m/s and her final velocity is 6 m/s, meaning there is a decrease in velocity. This decrease in velocity is known as deceleration or negative acceleration. To calculate the acceleration, we can use the formula:

Acceleration = (Final velocity - Initial velocity) / Time

In this case, we do not have information about time, so we cannot directly calculate the acceleration. However, we can use the fact that the skater slows steadily to determine the time it takes for her to slow down from 8 m/s to 6 m/s.

We know that the distance she travels on the rough ice is 5 m, so we can use the formula:

Distance = (Initial velocity + Final velocity) / 2 * Time

Substituting the values we know, we get:

5 m = (8 m/s + 6 m/s) / 2 * Time

Simplifying, we get:

5 m = 7 m/s * Time

Time = 5 m / 7 m/s

Time = 0.714 s

Now, using the value of time, we can calculate the acceleration using the first formula:

Acceleration = (Final velocity - Initial velocity) / Time

Substituting the values we know, we get:

Acceleration = (6 m/s - 8 m/s) / 0.714 s

Acceleration = -2 m/s^2

Therefore, the acceleration of the speed skater on the rough ice is -2 m/s^2. This negative value indicates that she is decelerating or slowing down. It is important to note that acceleration is a vector quantity, meaning it has both magnitude (in this case, 2 m/s^2) and direction (in this case, opposite to the initial velocity).

In conclusion, the speed skater's acceleration on the rough ice is -2 m/s^2. This shows that even though she was initially moving at a constant speed, the rough ice caused her to slow down due to the friction between her skates and the ice. Understanding the concept of acceleration helps us to better understand the forces at play in situations like this and how they affect the motion of objects.