I don't understand why it isn't. Forget the initial velocity? But that doesn't work either. ||v(t)|| ∝ s(t)-s(0),
so v(t) = k*(s(t)-s(0)). -> v(t)/k +s(0) = s(t), s'(t) = v(t). -> d/dt(v(t)/k + s(0)) = v(t), v(t) -> 0
EDIT: okay so I took the integral of v(t) and set it equal to v(t)/k +s(0)...
It's the average velocity which would have units of distance/ time multiplied by time so it would be the distance as a function of time.
So s(t) = c(v(t)-v(0)) (rearrangement of v(t) = v(0) + k*s(t) with 1/k = c )
Alright, so if I'm understanding this correctly ds(t)/dt = v(t), and therefore...
Homework Statement
The speed of a falling body might be based on the observation that the velocity of a falling object seems to increase the further it has fallen. Model the hypothesis "The speed of a falling object is proportional to the distance it has fallen" as a differential equation...