a 55kg skateboarder on a 3kg board starts coasting on level ground at 8 m/sec. Let k=3.2 kg/sec. About how far will the skater coast before reaching a complete stop?

Answer 1

What does k represent? Air friction resistance that is proportional to velocity?

Write and solve the differential equation of motion, to get equations for X(t) and V(t). Find the t when V = 0. Use that t for the location.

The assumption that resistance is proportional to velocity may not lead to an accurate result. As velocity slows down, the frictional resistance goes to zero with that assumption.