# How to calculate a change in velocity as a result of friction?

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.

• You need mass m for , Frictional force $F_f =\mu_k mg$... – Nehal Samee Mar 10 '18 at 8:31
• The mass cancels out because $a=F/m$ – Yuzuriha Inori Mar 10 '18 at 8:32
• And do you need the final velocity? Your question is a bit confusing on that part – Yuzuriha Inori Mar 10 '18 at 8:33
• @YuzurihaInori Hi, sorry for that. I'm trying to calculate the final velocity once it's reached the d distance. – Marko B Mar 10 '18 at 8:34
• That's right too....With final velocity $v$ he gets $a$ , so why need $\mu_k$ ? – 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 $v=\sqrt{u^2-2ad}$.