Using Equations for Linear Motion at Constant Acceleration

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The discussion focuses on the use of equations for linear motion at constant acceleration, specifically addressing when to apply the equations x = x(initial) + V*t and V(av) = 1/2(V(initial) + V). The first equation is applicable for constant velocity motion, which is a special case when acceleration is zero. The second equation is relevant for calculating average velocity during constant acceleration. While the original poster questions the importance of these equations, it is clarified that they are already encompassed within the broader context of motion equations. Understanding these distinctions is crucial for accurately applying the equations in physics problems.
Miike012
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When would I use the following equations?

x=x(initial) + V*t

V(av) = 1/2( V(initial) + V)

These equations are used for objects moving in a linear motion at constant acceleration correct?

my book says that I will most likely use the following equations...


but why are the two above equation not important?
 

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Miike012 said:
When would I use the following equations?

x=x(initial) + V*t
This one's for constant velocity motion. Note that it's a special case of the second equation on your list, when a = 0.

V(av) = 1/2( V(initial) + V)
This is good for constant acceleration. Note that it's related to the third equation on your list, which is just distance = average velocity X time.

These equations are used for objects moving in a linear motion at constant acceleration correct?
The first has acceleration = 0, but the second one is very useful.

my book says that I will most likely use the following equations...


but why are the two above equation not important?
They are already included, as I note above.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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