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We demonstrate a terahertz time-domain spectroscope for spatially resolved pump-probe experiments which are based on terahertz probe pulse generation with a photo-conductive switch synchronized to the pump pulse generation of a nanosecond laser. The accessible pump-probe delay ranges from 600 ps up to 200 μs. The spatial resolution of the spectroscope is better than 50 μm. We use the measurement system for spatially resolved lifetime mapping of photo-induced carriers in thin silicon in dependence on the photoexcitation intensity of the pump laser. At an optical pump intensity of 70mW/cm^2, we measured a carrier lifetime of 15.7 μs for silicon with 200 μm thickness and a much shorter carrier lifetime of 233 ns for 30 μm thick silicon.