Consider F=f(t), mv=
∫f(t)dt +c
Consider F=g(x), 1/2(mv^2)=
∫g(x)dx +k
Consider F=f(t), ɪ=
∫f(t)dt between t2 and t1, where velocity is u at t1 and v at t2.
Consider F=g(x), 1/2(mv^2)/1/2(mu^2)=
∫g(x)dx between x2 and x1 where velocity is u at x1 and v at x2