Expanding the range of variables

[Guest]

Hello,

I thought up a math problem, and hope you all will find it interesting.

There are two constants, k1 and k2, and two variables, s and s. Find a set of equations that can:
1. calculate the value for a if values for k1, k2 and s are known
2. calculate the values for s and k2 if values for k1 and a are known.

The ratio a/s can be a constant as well (a/s = const. may even be a requirement for the equations to work), but I would be interesting to see is there a possibility of a/s not being constant.

Inspiration for this problem comes from equations of motion when acceleration is constant. If we know values for initial speed u and final speed v, there is only one solution for values of displacement s and acceleration a in a given time interval t. Meaning, if u, v and t are known, a and s can’t have a range of proportional values in respect to one another, but only one exact value for each of them.

In the problem, I made values for u and v constant, so that the range of values for a and s could potentially be explored more freely. In a more broader context, I want to know is there a set of equations that can expand the range of given variables (a, s) and satisfy the conditions postulated in the problem. I’m hoping that the equations will be fairly simple, like the ones for motion.

Is it possible to find a solution for this problem?

[HallsofIvy]

Hello,

I thought up a math problem, and hope you all will find it interesting.

There are two constants, k1 and k2, and two variables, s and s.

I presume you mean "a and s".

Find a set of equations that can:
1. calculate the value for a if values for k1, k2 and s are known

To find one value you need one equation. Something as simple as a= k1+ k2+ s will do.

2. calculate the values for s and k2 if values for k1 and a are known.

Now you need two equations. s= k1+ a, k2= k1- a will do.

The ratio a/s can be a constant as well (a/s = const. may even be a requirement for the equations to work), but I would be interesting to see is there a possibility of a/s not being constant.

Inspiration for this problem comes from equations of motion when acceleration is constant. If we know values for initial speed u and final speed v, there is only one solution for values of displacement s and acceleration a in a given time interval t. Meaning, if u, v and t are known, a and s can’t have a range of proportional values in respect to one another, but only one exact value for each of them.

In the problem, I made values for u and v constant, so that the range of values for a and s could potentially be explored more freely. In a more broader context, I want to know is there a set of equations that can expand the range of given variables (a, s) and satisfy the conditions postulated in the problem. I’m hoping that the equations will be fairly simple, like the ones for motion.

Is it possible to find a solution for this problem?

As you have stated it, it is pretty close to being trivial and the equations are as simple or as difficult as you like.