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The rate (or velocity) of the hydrologic cycle affects water availability for agriculture, energy production, and planning for droughts or floods. Therefore, acceleration in the velocity of the hydrologic cycle is likely to impact multiple hydrological domains and management practices. Previous work has primarily studied hydrological cycle velocity and acceleration through the lens of flux magnitudes and their change. Motivated to expand this definition to characterize temporal coupling between stages in the hydrological cycle, we introduce novel definitions of hydrological cycle velocity and acceleration derived from the concept of drought propagation. We define hydrological cycle velocity as the response time between the 1-month Standardized Precipitation Index (SPI) and the 1-month Standardized Soil Moisture Index (SSI), and define acceleration as the change in response time between an early time period and a late time period. Using gridded reanalysis data from 1951-2020 and aggregation periods of 1 month, i.e., 1-month SPI and 1-month SSI, we analyzed summer (June, July, August) response times. Response times exceeded 100 days in southwestern CONUS (indicating a slower hydrological cycle velocity), and were substantially shorter elsewhere (10-20 days, indicating a quicker hydrological cycle velocity). Regarding potential acceleration between an earlier (1951-1985) and later (1986-2020) period, 16.94% of reanalysis grid cells experienced a significant deceleration (lengthening of response time) of their local summer hydrological cycle, while 17.34% of grid cells experienced a significant acceleration (shortening in response time). However, an analysis of decadal trends at the NCEI climate division scale showed no significant change, suggesting observed accelerations and decelerations were localized rather than regional. By framing hydrological cycle acceleration in terms of propagation of meteorological anomalies to land surface anomalies, we expand the conceptual basis for diagnosing changes in the hydrological cycle. Our results indicated evidence for regionally variable acceleration and deceleration from 1951-2020, but did not support a consistent hypothesis of summertime acceleration or deceleration at a larger scales.