5
$\begingroup$

I've been having trouble sorting this one out. I need to compute the time it will take for a vehicle traveling along a straight line to reach a particular point. I have the initial velocity ($v_i$), acceleration ($a$), and distance ($dx$) to the point. I don't have the final velocity $v_f$ nor the time $t$ I've been trying to solve this equation for time ($t$) but that's where I'm stuck.

$$ dx = v_it + {1\over2}at^2$$

$\endgroup$
4
$\begingroup$

You know everything except t in this equation. Therefore you should be able to re-arrange the equation into the form at^2 + bt + c = 0, the quadratic form. From there, you need to solve the quadratic (using the quadratic formula for example) to get two solutions for t. Since negative t does not make sense in this context, your answer will be the positive value for t.

$\endgroup$
  • $\begingroup$ Well, it's possible to get two positive solutions, in case $a$ and $dx$ have opposite signs. The desired answer is probably the smallest positive solution. $\endgroup$ – Rahul Dec 26 '12 at 16:39
  • $\begingroup$ In this case $dx$ and $v_i$ are positive but $a$ can be negative. $\endgroup$ – progrmr Dec 26 '12 at 21:49
  • $\begingroup$ It looks like there may also be the case where there is no real solution (where the discriminant < 0). I'll have to deal with that situation in the software also. Thanks! $\endgroup$ – progrmr Dec 26 '12 at 22:10
2
$\begingroup$

Use the Quadratic Formula. ${}{}{}{}{}{}{}{}{}$

$\endgroup$
  • $\begingroup$ Thanks for the link, that's a very helpful page. $\endgroup$ – progrmr Dec 26 '12 at 22:11

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.