Asked by unowen
Suppose we are given an arbitrary form for the acceleration a(t) of a particle that starts from rest at r(t_i)=0. What would be the derivation of its' position at r(t_f):
a)(t_f - t_i)⌠t_f a(t)dt
⌡t_i
b) v(t_f)+v(t_i)/2 ((t_f-t_i))
c)⌠t_f dt ⌠t dt'a(t') ???????
⌡t_i ⌡t_i
a)(t_f - t_i)⌠t_f a(t)dt
⌡t_i
b) v(t_f)+v(t_i)/2 ((t_f-t_i))
c)⌠t_f dt ⌠t dt'a(t') ???????
⌡t_i ⌡t_i