work energy graph

[faith hopelove]

Question is from TBR Physics work energy chapter passage 8 number 55.

Attached is the question and the answer provided. Now my question is could they have used W=F*x where F would be the restoring force of a spring. I used 1/2mv^2=kx*x therefore v=x so the graph is linear. I guess I want to really know why they used PE of a spring.

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[Sammy1024]

They want to know the relationship when the energy of the car is moving (KE) and then when the car is completely stopped (PE). And then since the question is talking about the spring, you have to use equations for spring.

Usually you would do...

mgh = 1/2mv^2

But this is a spring questions so...

1/2kx^2 = 1/2mv^2 and then you simplify.

1/2kx^2 is the potential energy in things that haver periodic motion like springs.

 

[faith hopelove]

Oh I see...that makes sense.