I am trying to find distance between two bodies A and B ($s$) as a function of time ($t$) given acceleration ($a$) as a function of distance. My approach is to model the situation with a differential equation that i then can solve.

An object A is released, with initial velocity $0$, $d$ meters above a static body B. A accelerates towards (or away from) B with the acceleration $a(s)$.

Is it correct to express the displacement as $$s(t+\Delta t)=s(t)+v(t)\Delta t$$ or as $$s(t+\Delta t)=s(t)+v(t)\Delta t+\frac{a(s(t))\Delta t^2}{2}~?$$

Note: Here i let $\Delta t$ tend towards $0$.

  • $\begingroup$ Thank you to @Philip Wood. In other news, why am i getting downvoted? $\endgroup$ – Ola Apr 26 '17 at 10:26
  • $\begingroup$ I did not downvote, but the problem is not formulated clearly. For instance it is not clear (1) which of the two bodies has initial velocity $v_0$, (2) why B would accelerate towards A or away from it, (3) what you are trying to calculate, (4) what you call displacement here? Also, are you familiar with differential calculus, because that's how a physicist would normally write these equations? $\endgroup$ – user1583209 Apr 26 '17 at 10:41

The first equation is a first order approximation which will be useful only if $\Delta t$ is very small (unless the acceleration is zero throughout the interval, in which case it is exactly correct). The second equation is a second order approximation, which will be useful (that is not too far out!) over larger time intervals, $\Delta t$, but is exactly correct if the acceleration is constant.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.