# The Rough Time...

**Classical Mechanics**Level pending

A rod is travelling on a smooth, level, horizontal surface. Beyond a point \(A\), the floor ceases to be smooth and the coefficient of friction is \(\mu = 0.1\). The rod is moving such that is moving towards the point \(A\). The front end of the rod crosses the point \(A\) at \( t=0\) with a velocity \(v_{0}\).

If at \(t= t_{0}\), the rod stops, find the value of \(t_{0}\) to the **nearest integer** .

**Details and assumptions:**

The length of the rod is \(10 m\).

The rough patch is sufficiently long.

The magnitude of acceleration due to gravity is \(9.8 \text{ } m/s^2\)