Key equations for finding acceleration include Newton's second law, f = ma, and the relationships involving distance, velocity, and time. Acceleration can be expressed as a = d(v)/dt, indicating it is the derivative of velocity with respect to time. Additionally, acceleration is the second derivative of distance, d, with respect to time. In vector form, acceleration is represented as \vec a = \frac{dv_x}{dt} i + \frac{dv_y}{dt} j + \frac{dv_z}{dt} k, where i, j, and k are unit vectors in the x, y, and z directions, respectively. These equations provide a comprehensive understanding of how to calculate acceleration in various contexts.