Calculating Work Conceptual Question

[BugsSport]

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.

 

[Doc Al]

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?

 

[baba89]

However, if the force is different for each situation, then the answer would not be Wo/2.

I would approach this problem by using the definition of work, which is the force applied multiplied by the displacement. In this case, the force applied to the car would be the same in both situations as it is being accelerated from rest to the same final velocity. Therefore, the work required to accelerate the car from rest to v/2 would also be Wo/2. This is because the displacement, or distance traveled, in both situations would also be different. In the first scenario, the car would travel a distance d to reach the final velocity v, whereas in the second scenario, the car would only travel a distance d/2 to reach the final velocity v/2. Therefore, the work required would be half of the original amount, Wo/2.

In summary, the work required to accelerate a car from rest to v/2 would be half of the work required to accelerate it from rest to v, assuming the force applied remains the same in both situations. This is because the displacement is also halved in the second scenario.