Advanced video frame interpolation (VFI) algorithms approximate intermediate motions between two input frames to synthesize intermediate frame. However, they struggle to handle complex scenarios with curvilinear motions since they neglect the latent acceleration information between input frames. Moreover, the supervision of predicted motions are tricky because real ground-truth motions are available. To this end, we propose a novel framework for implicit quadratic video frame interpolation (IQ-009VFI), which explores latent acceleration information and accurate intermediate motions via knowledge distillation. Specifically, the proposed IQ-VFI consists of an implicit acceleration estimation network (IAE) and a VFI backbone, the former is to extract latent acceleration priors between two input frames to progressively upgrade linear motions from the latter in coarse-to-fine manner. Moreover, to encourage both components to distill more acceleration and motion cues oriented towards VFI, we propose a knowledge distillation strategy in which implicit acceleration distillation loss and implicit motion distillation loss are used to adaptively guide latent acceleration priors and intermediate motions learning, respectively. Extensive experiments show that our proposed IQ-VFI can achieve state-of-the-art performances on various benchmark dataset