The proposed Hall D detector at Jefferson Lab (JLab) will have a time-of-flight detector composed of long and narrow scintillator strips. We have evaluated the time resolution of two strip prototypes in particle beams at the Institute for High Energy Physics (IHEP) in Protvino, Russia. The strips are 2.0m long and have square cross sections of size (2.5cm)^2 and (5.0cm)^2 respectively. In this paper we present results on how the signal size, timing, and time resolution of each of these strips depend on the entry position of the beam into the scintillator, on the material used for scintillator wrapping and on the phototube used for the readout.