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We use time-resolved terahertz spectroscopy to probe the ultrafast dynamics of the insulator-metal phase transition induced by femtosecond laser pulses in a nanogranular vanadium dioxide (V02) film. Based on the observed thresholds for characteristic transient terahertz dynamics, a phase diagram of critical pump fluence versus temperature for the insulator-metal phase transition in V02 is established for the first time over a broad range of temperatures down to 17 K. We find that both Mott and Peierls mechanisms are present in the insulating state and that the photoinduced transition is nonthermal. We propose a critical-threshold model for the ultrafast photoinduced transition based on a critical density of electrons and a critical density of coherently excited phonons necessary for the structural transition to the metallic state. As a result, evidence is found at low temperatures for an intermediate metallic state wherein the Mott state is melted but the Peierls distortion remains intact, consistent with recent theoretical predictions. Finally, the observed terahertz conductivity dynamics above the photoinduced transition threshold reveal nucleation and growth of metallic nanodomains over picosecond time scales. [ABSTRACT FROM AUTHOR]