The memory requirement of at-scale deep neural networks (DNN) dictate that synaptic weight values be stored and updated in off-chip memory such as DRAM, limiting the energy efficiency and training time. Monolithic cross-bar/pseudo cross-bar arrays with analog non-volatile memories capable of storing and updating weights on-chip offer the possibility of accelerating DNN training. Here, we harness the dynamics of voltage controlled partial polarization switching in ferroelectric-FETs (FeFET) to demonstrate such an analog synapse. We develop a transient Presiach model that accurately predicts minor loop trajectories and remnant polarization charge (Pr) for arbitrary pulse width, voltage, and history. We experimentally demonstrate a 5-bit FeFET synapse with symmetric potentiation and depression characteristics, and a 45x tunable range in conductance with 75ns update pulse. A circuit macro-model is used to evaluate and benchmark onchip learning performance (area, latency, energy, accuracy) of FeFET synaptic core revealing a 103 to 106 acceleration in online learning latency over multi-state RRAM based analog synapses.