The formula for velocity is defined as v(t) = dx/dt, representing the rate of change of position over time. Acceleration is given by a(t) = dv/dt or a(t) = d²x/dt², indicating the rate of change of velocity. Average velocity can be calculated using <Velocity> = Δdistance/Δtime, while average acceleration is <Acceleration> = ΔVelocity/Δtime. It's important to note that velocity is a vector quantity, incorporating both magnitude and direction, whereas speed is a scalar. The discussion clarifies the distinction between instantaneous and average values for both velocity and acceleration.