# Complete Square + Leibniz question (2 questions)

## Homework Statement

1. How did they complete the square for these equations in the picture below? What was their thought process?

2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out?

When you divide, how does it cancel out to give you a time unit?

## Homework Equations

1. In picture

2. ds/dt / d2s / dt2

## The Attempt at a Solution

1. It seems like it came out of thin air.

2. dt/ds = time?

#### Attachments

• completesq.jpg
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BiGyElLoWhAt
Gold Member
What is 2. in your relevant equations?

##V = d/t \to t = d/V##
You can add A and subtract A (equivalent to adding 0), and it's still the same.
##\frac{v_{y0}x}{v_{x0}} - \frac{gx^2}{2v_{x0}^2} + \frac{v_{y0}^2}{2g} - \frac{v_{y0}^2}{2g} ##
They factored out ## \frac{-g}{2v_{x0}^2} ##

Rearrange it and it might look a little closer.

In my relevant solutions it is velocity/acceleration, the way I put it was just in leibniz notation in terms of s(t)

BiGyElLoWhAt
Gold Member
I think I was just confused by all the slashes. Sort of makes it look like one big fraction made of fractions.

V2y0/2g

How did you find that

haruspex