How Do You Linearize the Equation d=vit + 1/2at^2?

[daewoo]

Homework Statement

basically I am suppose to linearize d=vit + 1/2at^2 into d/t^2 vs 1/t, t/d vs t^2/d and 1/d vs 1/t
and its asking which graphs would be linear and non-linear.

Homework Equations

d=vit + 1/2at^2

The Attempt at a Solution

all i know is that in order to linearize this i need to make it into the format y=mx+b from there i can see which variables alternate and which remain constant.
now I am confused on how I am suppose to get d/t^2 vs 1/t for the first one so i started to solve for t but i ended up needing to use the quadratic equation since its ax^2 + bx + c=0 but that really didnt help me since i coudlnt isolate "d" again. So basically I am kinda lost on how to manipulate this formula.

 

[learningphysics]

For the first part, I'd let y = d/t^2, let x = 1/t. Can you get the d and t equation into an equation with y and x... substitute appropriately and manipulate the formulas.

 

[Mindscrape]

If you divide the equation by t^2 you get

$$\frac{d}{t^2} = \frac{v_i}{t} + \frac{1}{2}a$$

If you wanted that against 1/t, basically make x a substitution of 1/t, you would have a graph that looked pretty linear with a slope of vi.

Do you see how it works?