# How can I derive the acceleration from 2 coordinates?

I am trying to derive the acceleration between 2 points. For example if I had (90.39, 44.99), (90.4, 44.97) and the time span was 0.1s. I get how to calculate the speed but how could I calculate the acceleration from this?

• Welcome to Physics SE! have you heard of the "suvat" equations - or the equations of motion for constant acceleration? – Alex Robinson Nov 19 at 16:58
• You can’t. You require information about how the journey progressed in terms of its velocity. – Jake Rose Nov 19 at 17:00
• @AlexRobinson I have but its been 8 years since I used them. Would you recommend I read something to understand this? – soccer_analytics_fan Nov 19 at 17:06
• @JakeRose what do you mean by that? Could you provide me a link I could read that would help me understand how the journey progresses in terms of velocity. – soccer_analytics_fan Nov 19 at 17:07
• Alex's answer is useful, but I'd take head to my comment. – Jake Rose Nov 19 at 17:53

You can’t. You require information about how the journey progressed in terms of its velocity

Whilst this is a technicality, it is entirely correct - you would need to know the initial velocity or the final velocity in order to truly answer this question.

However, it seems implicit to take the initial velocity to be zero in this case - in which case we are solving for acceleration and so will use the equation: s = u*t + 1/2*a*t^2.

where: s = displacement, u = initial velocity, a = acceleration and t = time taken.

Displacement is calculated by finding the root of the sum of the squares of the differences between the x and y values for the coordinates you've posted. (a^2 +b^2 = c^2)

And from there, calculating the answer is trivial.

• It's worth noting this makes the implicit assumption of constant acceleration. You could have some function $a(t)$ which is not constant and over the time period only averages to the result you give. – Jake Rose Nov 19 at 17:50

No, you cannot without further assumptions and information.

You can't even calculate the speed. You can only calculate the average speed and by the first theorem of calculus that the body would have this speed at least at one time frame, but can have different speeds otherwise.