The derived functions were suitable because both s and v were functions of t and the resulting equation therefore contained only two variables (either s and t, or v and t).

In practice the acceleration of a moving object is more likely to depend on the distance or speed rather than the time of motion. For instance, the tension in an elastic string depends on the extension, so the force acting on a particle attached to the end, and hence the acceleration of that particle, depends on its displacement from the natural length position. In such cases, where the acceleration is not a function of time, we may have to find an alternative derived function to represent acceleration.