Velocity as a function of time?

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To determine the velocity of an object with a constant acceleration of 22.3 m/s² at an angle of 63.9 degrees East of South, one must derive a function v(t) that represents velocity over time. The relevant equation is v = v₀ + at, where v₀ is the initial velocity at time t=0 and a is the acceleration. It is crucial to recognize that velocity is a vector quantity, meaning both magnitude and direction must be considered. Clarification was provided that v₀ should not be confused with acceleration but rather the initial velocity. Understanding these concepts is essential for accurately calculating velocity as a function of time.
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if an object has an acceleration of 22.3 m/s^2 [63.9 degrees E of S]

what is its "velocity as a function of time"

not sure what that means.. any ideas?
 
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bullroar_86 said:
if an object has an acceleration of 22.3 m/s^2 [63.9 degrees E of S]

what is its "velocity as a function of time"

not sure what that means.. any ideas?

It means you have to find a function v(t) that relates the speed of the object, and the time elapsed.

Hint: The answer is in the definition of (constant) acceleration.
 
v=vnot+at
vnot equals acceleration from the beginning of the problem.
v= velocity at a given time.
 
ayalam said:
v=vnot+at
vnot equals acceleration from the beginning of the problem.
v= velocity at a given time.

No, in that equation, "vnot" has to be the velocity at t= 0. And be sure to note that the velocity is a vector, not just a number.
 
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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