The kinematics of locomotion toward a goal

A mathematical model is developed that treats rats in runways as uniformly accelerated bodies. The purpose of the model is to permit conversion of the continuously varying measures of runway speeds at different points in the alley into three invariant parameters of performance: start latency, acceleration, and brakepoint. This simple model fits most of the data examined, and changes in the parameters throw new light on phenomena such as the partial reinforcement acquisition effect. In particular, it is shown that partially reinforced rats accelerate faster but cease accelerating earlier in the runway than do continuously reinforced rats. This explains the qualitative differences often found between start and goal speed measures. The analysis takes as its unit patterns of terminal behavior rather than the rate of the responses that constitutes them, and thus may permit coherent treatment of instrumental and operant behavior.