Is this assumption correct? (dynamic friction)

[aps0324]

A particle of mass M slides on a horizontal surface with coefficient of (dynamic) friction
μ = 0.4. At time t = 0 it is 1m from a vertical wall, moving at 6 m/s perpendicularly towards it. When does it strike the wall? ( You may assume it is less than 1 second)

Homework Equations

friction = μ x N

where N is the normal force

suvat equations

The Attempt at a Solution

friction = μ x N

M x a = μ x M x g where g = 10 m/s^2

a = 0.4 x g = 4 m/s^2

I want to know if I can take this as a deceleration? Therefore hitting the wall with a velocity of :

v^2 = u^2 + 2as where u = 6 m/s s = 1m a = -4 m/s^2

v = 5.29 m/s

and where the time taken is :

v = u + at

t = 0.1775 seconds

 

[Hootenanny]

I've not checked your arithmetic, but your method looks fine to me.

One minor point: you have used two SUVAT equations here. However, if you would have used the equation s = ut + ¹/₂at², you could have cut your working in half.

 

[nlightner]

Yes, your assumption that the particle will decelerate towards the wall is correct. However, your calculation for the time taken is incorrect. You should use the equation s = ut + 1/2at^2 to find the time taken instead of v = u + at. Using this equation, the time taken would be approximately 0.32 seconds.