Mechanics MC question

[tazza]

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Can somebody please help me with this question? I understand that I need to use F = ma but I don't really understand the concept of what the question is asking for v1. Is it like euler's formula?

[HarveyD]

start off with F = ma
get it in terms of a
then use the formula relating v and x to a
i.e.
a = (1/2 v^2)d/dx

edit: whats the answer btw?

[illuminati]

tough question, I think its D
but basically I think it should be like this
F(x) = the force applied
so a = F(x)/m
therefore d/dx(v^2/2) = F(x)/m
therefore you have (v^2)/2 = integral: F(x)/m dx
here's where it gets a bit weird
Integral:F(x)/m dx will give you the change in velocity
so therefore
(v1)^2/2 - (v0)^2/2 = definite integral: F(x)/m dx with terminals x0 and x1
times both sides by 2, move v0^2 and square root
Therfore, should be D.

[Mao]

For people who are doing physics, you can approach this from an energy perspective:

The force is doing work on the mass, which increases the kinetic energy.




Work is defined as force times distance (if force is constant). For a variable force, it would therefore make sense for it to be defined as an integral:

The answer is therefore D.

[tony3272]

Ha i did that exam during school today. Added v_o rather than v_o²   

[costa94]

fund theorem and d/dv 1/2 v^2 combined