Question

A 34 kg block is sliding on a frictionless surface at a rate of 25 m/s. It enters a surface that has a coefficient of kinetic friction of .35. How long does it take the block to stop and how far does it slide before it comes to a stop after it enters the surface with friction?

Answer 1

First, apply law of conservation of energy: the kinetic energy turned into work done against friction.

$$\frac12mv^2=\mu mgx,\\\space\\ x=\frac{v^2}{2\mu g}=91\text{ m}.$$

How much time will it take?

$$t=\frac{2d}{v_i}=7.28\text{ s}.$$