Solution:

Consider a simple path i.e. from $w^0$ to $w^1$ an interpolated motion between two-knot points $w^0$ to $w^1$.

The equation for the path from $w^0$ to $w^1$ is represented by

a cubic polynomial given by $\mathrm{w}(\mathrm{t})=\mathrm{a} \mathrm{t}^3+\mathrm{bt}^2+\mathrm{c} t+\mathrm{d} ; 0 \leq \mathrm{t} \leq \mathrm{T} ; \mathrm{T}\gt0$; where $\mathrm{w}(\mathrm{t})$ is …