How to make an equation

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.

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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.

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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