Finding Velocity at a Given Time on an Acceleration v Time Graph

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To find the velocity at a specific time (t=5 sec) on an acceleration vs. time graph, the area under the curve from t=0 to t=5 must be calculated. This area represents the change in velocity, and integrating the acceleration function can also yield the velocity at that time. If the area calculation is incorrect, it may be due to misinterpretation of the graph or the limits used. The correct approach involves ensuring the area under the curve is accurately determined within the specified time frame. Properly applying these methods will yield the correct velocity value.
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Homework Statement



The problem is, to find velocity at a given time (t=5 sec) on a acceleration v time graph.

Homework Equations


The Attempt at a Solution


I think the area under the curve represents the average velocity, but I really do not know how to find the velocity at THAT given time.

*Note: I included a picture on the bottom, I tried to find the area under the curve but did not come up with the correct answer. It is the graph labled Particle C
 

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area under the curve is the velocity.
 
You either

1. Integrate acceleration up to t=5 if acceleration is given as a function of t OR

2. Find the area under the curve within t=0 and t=5 inclusive
 
attachment is included.
 
85 ms-1 is incorrect?
 
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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