Calculating Work Conceptual Question

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To accelerate a car from rest to a speed v, a certain amount of work Wo is required. The discussion revolves around determining the work needed to accelerate the car to half that speed, v/2. It is suggested that if the force remains constant, the work required would be Wo/2, similar to the case of distance. However, the Work-Energy theorem is invoked to clarify that the relationship between speed and work is not linear, indicating that the work required for v/2 is actually less than Wo/2. The conversation emphasizes the importance of understanding the implications of the Work-Energy theorem in this context.
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Homework Statement


A certain amount of work Wo is required to accelerate a car from rest to a speed v. How much work is required to accelerate the car from rest to v/2?

Homework Equations


W = Fd


The Attempt at a Solution


I know that if we were finding the distance instead of velocity, then the answer would be
Wo/2, but I'm not sure if the force is the same for each situation. If it is, then I assume that the answer would also be Wo/2.
 
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BugsSport said:
I know that if we were finding the distance instead of velocity, then the answer would be
Wo/2, but I'm not sure if the force is the same for each situation. If it is, then I assume that the answer would also be Wo/2.
What makes you think the distance would be 1/2?

What does the Work-Energy theorem tell you?
 

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