Prominent models of time perception assume a reset of the timing mechanism with an explicit onset of the interval to be timed. Here we investigated the accuracy and precision of temporal estimations when the duration does not have such an explicit onset. Participants were tracking a disc moving on a circular path with varying speeds, and estimated the duration of one full revolution before the stimulus stopped. The onset of that revolution was either cued (explicit), or undetermined until the stimulus stopped (implicit). Reproduced duration was overestimated for short and underestimated for long durations, and variability of the estimates scaled with the duration in both temporal conditions. However, the bias was more pronounced in the implicit condition. In addition, if the stimulus path was partially occluded, duration of the occluded motion was correctly estimated. In a second experiment, we compared the precision in the explicit and implicit conditions by asking participants to discriminate the duration of one revolution before the stimulus stopped to that of a static stimulus presentation in a forced-choice task. Sensitivity of discrimination was worse in the implicit onset condition, but surprisingly, still comparable to the explicit condition. In summary, the estimates follow principles described in prospective timing paradigms, although not knowing beforehand when to start timing decreases sensitivity of temporal estimations. Since in naturalistic contexts, we often do not know in advance which durations might be relevant to estimate, the simple task presented here could become a valuable tool for testing models of temporal estimation.