A motorcycle of mass m starting from rest can attain a speed v after work W is performed by its engine.If the engine could perform work 4W then the final speed would be? A)4v B)2v C)16v D)(2v)^1/2 E)(4v)^1/2

Question

Quizplus · Accepted Answer

The work done by the engine is equal to the change in kinetic energy of the motorcycle. Let's call the initial speed of the motorcycle U and the final speed v. Then we have:

W = (1/2)*m*v^2 - (1/2)*m*U^2

If the engine could perform 4W work, then the final speed would be:

4W = (1/2)*m*v'^2 - (1/2)*m*U^2
v'^2 = 8W/m + U^2
v' = sqrt(8W/m + U^2)

So the final speed would be greater than v, but not four times greater. We can see this by considering the extreme case where W = 0. In this case, the final speed would be equal to the initial speed, v' = U, which is not four times greater than v.

Therefore, the best choice is B) 2v, since it is the only option that is smaller than A) 4v and consistent with the idea that the final speed would be greater than the initial speed but not four times greater.

A Motorcycle of Mass M Starting from Rest Can Attain