quick question

[Zebra]

I understand your steps but I'm questioning why d(1/2 v^2) /dx cannot be used?

VCAA says d(1/2 v^2) /dx is fine but i just dont see getting v0^2 with this.
your steps make total sense but tbh i wouldn't have got it if this came up on the exam.

thanks. :S

[dc302]

You can use it!

We have F/m = d(1/2 v^2)/dx

We want to integrate both sides with respect to x, and also from x0 to x1.

But how do we do that with the RHS? Well we need to know this:

           integral from a to b of f(x)dx = F(b) - F(a)             ....(i'm sure you knew this)

So we will do exactly this. Note that if f(x) = d(1/2 v^2)/dx, then by definition, F(x) = 1/2 v^2

RHS = integral from x0 to x1 of d(1/2 v^2)/dx dx = 1/2 v(x1) ^2 - 1/2 v(x0) ^2

But we know that v(x1) = v1 and v(x0) = v0 (as stated in the question). So sub those in and you're done.