Velocity and Friction Question

[AshNZ]

Homework Statement

An object takes 18m to stop due to friction. Assume no skidding. If the coefficient of static friction is 0.35, what is the initial velocity of the object?

The Attempt at a Solution

I have looked at the Normal vs Frictional force equation and I have looked at the three equations involving initial, final velocity and acceleration. I've gone through my notes and skimmed through couple of other book but now help.

 

[Hao]

You can apply Newton's second Law to find an expression for Force, and apply your friction equation to find another expression for Force.

There will be unknown variables, but you will be able to find a numerical expression for acceleration, and hence a numerical answer for initial velocity.

However, I am not quite sure what is meant by 'stopping without skidding' unless it is a rotating object.

 

[nlightner]

Based on the given information, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. In this case, we know that v = 0 m/s (since the object has stopped) and a = -0.35g (since the object is being decelerated by friction). We also know that s = 18m. So the equation becomes 0^2 = u^2 + 2(-0.35g)(18m). Solving for u, we get u = √(0.35g*18m) = 6.07 m/s. Therefore, the initial velocity of the object was 6.07 m/s.