A truck of mass m moves along a horizontal test track subject only to a force resisting motion that is proportional to its speed. At time t = 0 the truck passes a reference point moving with speed U. Find the velocity of the truck both as a function of time and as a function of displacement from the reference point. Find the displacement of the truck from the reference point as a function of time.

Repeat these calculations for similar trucks subject to resistance forces proportional to

(a) Square root of speed;

(b) Square of speed;

(c) Cube of speed.

How long does the truck take to come to rest in each case? Draw plots of velocity against displacement in each case. Explain, in qualitative terms, the behaviour of the truck under each type of resistance.

How would you model mathematically a truck that is subject to a small constant resistance plus a resistance proportional to its speed? How far would such a truck travel before coming to rest, and how long would it take to do so? Can you repeat¥these calculations for trucks subject to a small constant resistance plus a resistance proportional to speed squared or speed cubed?

What general conclusions can you draw about the type of terms that it is sensible to use in mathematical models of engineering systems to describe resistance to motion?