Finding acceleration from velocity and postion

[mcwynne]

Hey all!
I'm really struggling with this question (image below) and have no idea where to start. I've tried using v(dv/dx)=acceleration and d/dx(1/2v^2) = acceleration, but I'm probably missing something.

Any help at all would be appreciated. Thank you so much!

 

[Deleted member 4993]

Hey all!
I'm really struggling with this question (image below) and have no idea where to start. I've tried using v(dv/dx)=acceleration and d/dx(1/2v^2) = acceleration, but I'm probably missing something.
View attachment 33321
Any help at all would be appreciated. Thank you so much!

Please show us - what did you get using

a = dv/dt = dv/dx * dx/dt

 

[mcwynne]

That's what I'm finding tricky... I can't seem to wrap my mind around how I'm supposed to separate the variables to do anything at all with that identity.

 

[Deleted member 4993]

That's what I'm finding tricky... I can't seem to wrap my mind around how I'm supposed to separate the variables to do anything at all with that identity.

First calculate dv/dx - using implicit differentiation.

 

[mcwynne]

Oh my goodness, as soon as you said implicit diff everything clicked. Thank you. I'll leave my solution below, if somebody would be able to check over to see if I've done anything wrong that would be so lovely. Thank you again, you're a lifesaver.