Velocity and Acceleration Extra Credit Problem

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The discussion centers on the kinematic equation d = Vi t + 1/2 at^2, which describes the relationship between distance, initial velocity, acceleration, and time. Participants clarify the meanings of the variables: d represents distance, Vi is initial velocity, a is acceleration, and t is time. The equation can be verified through calculus, suggesting that a calculus-based approach may be necessary for a thorough understanding. There is an emphasis on the average speed formula v = (Vf + Vi)/2 and its relationship to the kinematic equation. The conversation highlights the importance of clarity in presenting physics problems and solutions.
FreshmanInPhysics

Homework Statement


d=Vi t + 1/2at^2
What do each of these mean? Show that this is true

d=vt-Solve

v=Vf+Vi/2 - Substitute Vf with Vf= Vi+at

Homework Equations


v= average speed
Vi=initial speed
Vf= final speed

The Attempt at a Solution


Vit: This represents the initial velocity at said time elapsed
1/2at^2: This represents half the acceleration at said time elapsed squared

d/t=v

v=2Vi+at/2


 
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FreshmanInPhysics said:

Homework Statement


d=Vi t + 1/2at^2
What do each of these mean? Show that this is true

d=vt-Solve

v=Vf+Vi/2 - Substitute Vf with Vf= Vi+at

Homework Equations


v= average speed
Vi=initial speed
Vf= final speed

The Attempt at a Solution


Vit: This represents the initial velocity at said time elapsed
1/2at^2: This represents half the acceleration at said time elapsed squared

d/t=v

v=2Vi+at/2

Welcome to the PF.

Your post is a bit jumbled. Are you in a calculus-based physics class? Calculus is one way you can show that this equation is correct.
 
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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