The mathematical relationship between velocity and acceleration can be expressed in terms of distance by integrating the acceleration with respect to time.
Let's denote velocity as v(t), acceleration as a(t), and distance as d(t). The relationship between these variables can be described as follows:
Acceleration is the derivative of velocity with respect to time: a(t) = dv(t)/dt
Velocity is the derivative of distance with respect to time: v(t) = dd(t)/dt
To relate acceleration and distance, we can substitute equation 2 into equation 1: a(t) = d²d(t)/dt²
This equation represents the relationship between acceleration and the second derivative of distance with respect to time. It shows that acceleration is the rate of change of velocity, which, in turn, is the rate of change of distance.