This paper introduces a continuous-time fast motion estimation framework using high frame-rate cameras. To recover the high-speed motions trajectory, we inherent the bundle adjustment using a different frame-rate strategy. Based on the optimized trajectory, a cubic B-spline representation was proposed to parameter the continuous-time position, velocity and acceleration during this fast motion. We designed a high-speed visual system consisting of the high frame-rate cameras and infrared cameras, which can capture the fast scattered motion of explosion fragments and evaluate our method. The experiments show that bundle adjustment can greatly improve the accuracy and stability of the trajectory estimation, and the B-spline representation of the high frame-rate can estimate the velocity, acceleration, momentum and force of each fragments at any given time during its motion. The related estimated result can achieve under 1% error.