Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to make an equation If I know some points on the graph? I want to make an equation for a car which accelerates and graph it. For example I know that on the 0 second the car moves 0 km/h, on the 2 sec the car moves 5 km/h and so on. I need the equation so I can calculate instant velocity by differentiating the equation.

share|cite|improve this question
up vote 1 down vote accepted

The answer depends on the model you use. If you assume the constant acceleration then $$ v_t = v_0+at $$ where $v_0$ is an initial speed. So in your case $v_0 = 0$ and $v_2 = 5$ so easily $a = 2.5$

If you need an equation for the location of the car, then by integrating (or from the course of physics): $$ S_t = S_0+v_0t+\frac12at^2 = S_0+\frac54t^2 $$ where $S_0$ is a initial location. You can take equal to $0$ to put the car at origin from the beginning.

For the extension: $v_t = at$. In this case you assume the constant acceleration, i.e. you have the only unknown parameter. If you assume that an acceleration has more difficult structure with $m$ unknown parameters, you need to have $m-1$ more measurements.

share|cite|improve this answer
And what's the equation? – Cobold Sep 22 '11 at 16:35
@Cobold: There are now equations for location and for the velocity. Do you need another one? – Ilya Sep 22 '11 at 16:51
Maybe it's just notationally different than the/an equation that the OP was expecting. – The Chaz 2.0 Sep 22 '11 at 18:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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