If you have an object moving at u initial velocity with no acceleration, and a surface with a $$\mu_k$$ frictional coefficient, how can you calculate its final velocity after having traveled d distance over this surface?

Would I also need mass m to figure this out?

I've tried looking for a formula to help me out but unfortunately I was unable to find it... I'd really appreciate some help on the matter!

Thank you tons.

  • $\begingroup$ You need mass m for , Frictional force $F_f =\mu_k mg$... $\endgroup$ – Nehal Samee Mar 10 '18 at 8:31
  • $\begingroup$ The mass cancels out because $a=F/m$ $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 8:32
  • $\begingroup$ And do you need the final velocity? Your question is a bit confusing on that part $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 8:33
  • $\begingroup$ @YuzurihaInori Hi, sorry for that. I'm trying to calculate the final velocity once it's reached the d distance. $\endgroup$ – Marko B Mar 10 '18 at 8:34
  • $\begingroup$ That's right too....With final velocity $v$ he gets $a$ , so why need $\mu_k$ ? $\endgroup$ – Nehal Samee Mar 10 '18 at 8:34

The frictional force is $\mu_k mg$ opposite to $u$. We get a decelaration of $a=\mu_k g$ and this finally gives us $v=\sqrt{u^2-2ad}$.


  • $\begingroup$ @MarkoB You are always welcome. If you think this answers your question, please upvote and accept it so that others know that the answer is useful and correct. We are trying to reach a broader audience so this helps a lot. $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 8:40
  • $\begingroup$ Yep, just did! Am new to the site, so am not entirely sure how all of this stuff works. :) Appreciate the help. $\endgroup$ – Marko B Mar 10 '18 at 8:46
  • $\begingroup$ Its cool, and Welcome to Physics SE! $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 8:47
  • $\begingroup$ physics.stackexchange.com/tour . This might help you out. Accepting an answer means ticking that small tick mark beside the answer. $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 8:49

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