A particle of unit mass moves on a straight line under the action of a force which is a function ƒ(v) of the velocity v
of the particle, but the form of this function is not known.
A motion is observed, and the distance x covered in time t
is found to be connected with t by the formula
x = at + bt² + ct³, where a, b, and c have numerical
values determined by observation of the motion. Find the
function ƒ(v) for the range of v covered by the experiment.