How Do You Calculate the Total Displacement of a Car Accelerating Uniformly?

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To calculate the total displacement of a car accelerating uniformly, first, the initial speed (11.3 m/s) and final speed (18.5 m/s) are established, along with the time of acceleration (45 seconds). The acceleration is calculated as 0.16 m/s². The displacement during the acceleration phase is found using the equation v² = v₀² + 2a(x - x₀), resulting in a value of 670.5 meters. However, the total displacement for the entire trip, including the initial cruising phase, is actually 1.52 kilometers, highlighting the importance of considering all phases of motion in the calculation.
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Homework Statement



If a car cruises at 11.3m/s for 75s, then uniformly speeds up until, after 45s, it reaches a speed of 18.5 m/s, what is the car's displacement during this motion?

Homework Equations



v(1)=at+v(o)
v^2=v(o)^2 +2a(x-xo)

The Attempt at a Solution



V(o)=11.3
V(1)=18.5
t=45

a=7.2/45=.16

so by plugging in all this values into v^2=v(o)^2 +2a(x-xo) i get 670.5m

But they are telling me the answer is 1.52km
 
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nm solved it.. its asking for the displacement of the whole trip..

man i hate how the questions are worded in a tricky way.
 
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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