How Do You Isolate 'g' in the Equation s=ut+1/2at^2?

[Large dwarf]

As part of our data analysis, we need to find 'g' through a calculation and then back it up with graphical representation. Since I have 'u', 's' and 't', the choice of equation is rather simple: s=ut+1/2at^2. Then this needs to be converted so y=mx, it's by no means necessary, but I want to do it.

I got told that t^2= (2sy)/(ay)=(2/ay) x (sy) is the conversion for y=mx, yet I it doesn't seem right to me. I'm also not sure whether that value of 'y' is that graphical value of 'y', but it doesn't look like it to me.

 

[Nate810]

It's a bit confusing but if I'm understanding correctly, the equation you are looking for is s=ut+1/2at^2. To convert this equation to y=mx form you would use the following: y=(2s/a)x(u/2). This equation is useful for finding the value of 'g' (the acceleration due to gravity): g=2s/at^2. To graphically represent this equation, you can plot a graph of acceleration (in m/s^2) against time (in s). The slope of the line (m) will represent the value of 'g'.

 

[m2003]

First of all, it is great that you are using data analysis to solve for 'g' in this situation. As a scientist, it is important to use equations and data to support our findings and conclusions.

In order to solve for 'g', we need to rearrange the equation s=ut+1/2at^2 to isolate 'g'. This can be done by first subtracting ut from both sides, giving us 1/2at^2 = s-ut. Then, we can divide both sides by 1/2t^2 to get a = (2s-2ut)/t^2. Finally, we can substitute in the values of 'u', 's', and 't' to solve for 'g'.

As for the graphical representation, it is important to understand that the equation s=ut+1/2at^2 represents a parabolic curve. This means that as 't' increases, the value of 's' will also increase, but at a decreasing rate. The graphical value of 'y' would be the value of 's' on the y-axis and the value of 't' on the x-axis.

I am not sure where the conversion of t^2= (2sy)/(ay) came from, but it does not seem to be the correct approach. I would suggest using the equation a=(2s-2ut)/t^2 to solve for 'g' and then plotting the values of 's' and 't' on a graph to visually represent the parabolic curve.

Overall, it is important to carefully analyze the data and use the appropriate equations and methods to find the value of 'g'. I hope this helps and good luck with your data analysis.