Help on an acceleration problem (Deceleration?)?

[dranly1]

Homework Statement

A speed skater moving across frictionless ice at 8.7 m/s hits a 5.6 m -wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s.

What is her acceleration on the rough ice?

Homework Equations

(v1-v0)/t

The Attempt at a Solution

So I've attempted to determine the amount of time it takes her to get across the ice by dividing 5.6 m/s to 8.7 m/s getting .64 m/s to cross the rough patch. So the equation I tried was this: (6.0-8.7)/.64 = -7.59 which isn't correct. I'm in need of some help...

 

[klondike]

But the 8.7 m/s is the speed she moved before she hit the 5.6m patch. So the time taken to cross the patch is not 5.6/8.7.

 

[dranly1]

My thought was that since she was moving 8.7 m/s that it would take her less than a second to move across a distance less than 8.7 meters.

 

[collinsmark]

My thought was that since she was moving 8.7 m/s that it would take her less than a second to move across a distance less than 8.7 meters.

That's not necessarily true. It depends on how fast she slows down.

And like klondike mentioned, the t = x/v formula is only valid if she is traveling with a constant velocity. But that's not the case when she is on the rough patch of ice.

When she's on the rough patch of ice, she is traveling with uniform acceleration.

There is another kinematics equation/formula that you can use to solve this directly (or combine two of the other ones solve it that way, but that makes the problem more complicated).

There are some kinematics equations for uniform acceleration found here:
https://www.physicsforums.com/showthread.php?t=110015

Physics is a pretty neat area of study, because there are relatively few things that require memorization. That said, this set of kinematics equations for uniform acceleration are one of the exceptions that I strongly recommend that you memorize. You don't have to memorize much in physics, but do memorize these. (There are 4 kinematics equations for uniform acceleration that should be memorized. Not all of the equations in the link I provided relate to uniform acceleration kinematics.)

 

[Nickie]

Dear student,

Thank you for reaching out for help with this acceleration problem. From your attempt, it seems like you are on the right track, but there are a few things to consider.

First, the speed skater is decelerating (slowing down) as she crosses the rough ice, so the acceleration would be negative. This means that your final answer should be a negative number.

Second, you are correct in using the equation (v1-v0)/t to find the acceleration. However, the time (t) in this case should be the time it takes for the skater to go from 8.7 m/s to 6.0 m/s, not the time it takes to cross the rough patch. You can find this time by dividing the change in speed (8.7-6.0) by the initial acceleration of the skater (which is not given in the problem, but can be calculated using the equation a = (v1-v0)/t).

So, your final equation should look like this: a = (6.0-8.7)/((8.7-6.0)/a). This will give you the correct answer for the skater's acceleration on the rough ice.

I hope this helps and good luck with your problem solving! Remember to always double check your units and make sure they are consistent throughout your calculations. If you have any further questions, don't hesitate to ask.

Best,