Question

show that the total distance from the end of string for each nut increases according to the linear kinematics equations. String length is 2.5m. The first nut is at the tip of the string, the second is 9cm from the first, the thrid is 27cm from the second, the fourth is 45cm from the third, the fifth is 63cm from the fourth, and the sixth is 81cm from the fifth.

Answer 1

Do you have a diagram for it?

Answer 2

No I am totally lost on this

Answer 3

I'd start by first graphing the data as I've done here. You'll notice that it's a polynomial curve which can be modeled with the equation:
\[x_f=0.09x^2 - 0.18x + 0.09\]From there take a look at the kinematic equations and note that the above equation is similar to the equation for distance with a constant acceleration.