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[taggs-sasuke]

I'm sorry if it's really easy but can someone please explain the answer to me?

Show that:




Answer:

???

(I understand the rest.)

 

[Aerath]

d^2 x / dt^2
= dv/dt = dv/dx * dx/dt = dv/dx *v
= vdv/dx

Since v = d(1/2v^2)/dv

vdv/dx = d(1/2v^2)/dv * dv/dx
= d(1/2v^2)/dx

 

[Revacious]

its just chain rule

RHS = dv/dt

dv/dt = dv/dx times dx/dt

but dx/dt = v

so d^2/x / dt^2 = v dv/dx


and v = d/dx half v^2, you can verify by differentiating.

 

[shuning]

回复: Show that

this Q is weired.... usually they gona ask

instead of


infact i can never remembed using LOL

 

[taggs-sasuke]

Thanks!

 

[oly1991]

actually i've seen this come up a bit in past papers (particiularly from private schools)

Given v = dx/dt

d^2x/dt^2 = d/dt(dx/dt)
= dv/dt
= dv/dx.dx/dt
= dv/dx.v
= dv/dx.d/dv(1/2v^2)
= d/dx(1/2v^2)