Manipulating equations

[canadianofpeace]

Hi all last few problems I have here.

For the formula
Vf^2= vo^2 + 2ad

What is the relation between vf and a? Is it Vf=root a or Vf=root2a? I ask because I have trouble with the following

When comparing Vf of a projectile between the earth and the moon I am confused. If I wanted to have a ratio of Acceleration moon/Acceleration Earth, how do I set this up? Do I go Accel moon/Accel Earth = Root(1.666)/Root(10)?

Second, y=-1/x is the relation between y and x negative or just a regular reciprocal?


Thanks

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[NextStepTutor_1]

With regards to the equation - if the initial velocity is zero then the equation can be manipulated into the following:

vf = (2a∆x)1/2
So as the acceleration increases, the final velocity increases but not to the same magnitude b/c the square root of the acceleration is being taken (acceleration is proportional the square of the final velocity). For example, if the acceleration were increased 100x, the final velocity would only increase 10x.
The "2" in the equation could be thought of as a constant for simplicity's sake - it will not change. Keeping this bit of info in mind, when you are comparing two like equations in the form of a ratio (in this case the final velocity of a projectile in terms of the acceleration due to gravity on the moon compared to the acceleration due to gravity on Earth) all constants will cancel out - the "2" in the numerator will cancel out the "2" in the denominator. If the distance (∆x) is the same then, as you wrote, the ratio would be root(1.66)/root(10) in terms of the final velocities b/c the acceleration due to gravity is the only changing component between the two environments (presuming the objects falling are the same).


As for y=-1/x the relationship is negative and reciprocal. You can think test this by plugging in numbers for each variable.
If y = 1 then x = -1
If y = 2 then x = -.05
etc.




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