Kinematic equation without time

[Bakatota]

I understand most of the kinematic equations, but there is just this one equation that omits time from the equation. I always end up with V₀²+2a(x - x₀) = 2V₀V + V²

The 2V₀V part is what I don't understand how to get rid of. So if you please could you do the equation with steps , I would be very grateful. Thank you.

 

[Ibix]

What are the steps you took to get to that equation?

 

[Bakatota]

t = (V - V₀)/a

x - x₀ = V₀((V-V₀)/a) + .5a((V - V₀/a)²)

x - x₀ = (V₀V - V₀²)/a + (V² + V₀²)/2a

2a(x - x₀) = 2V₀V -2V₀² + V² +V₀²

V₀²+2a(x - x0) = 2V₀V + V²

 

[Ibix]

What do you get if you expand ##(V-V_0)^2##?

Edit: By the way, something seems to be wrong with the brackets in the last term of your second equation. I assumed that was just a typo, but if they look right to you then you need tk think about that too.

 

[Bakatota]

Oh I see what I did wrong. As you intimated, I did not expand (V - V₀)² correctly. Now I have -2V₀V to cancel out.

 

[Ibix]

That's right. Algebraic slips can be hard to spot. I sometimes write each term on a separate line when I'm expanding brackets, which makes it easier for me to not get distracted when I'm doing it. Then when I'm collecting terms together I put a little tick above each one as I copy it on to the next line so I don't lose one or double one up by accident. You can also count terms. You know that ##(V-V_0)^2## should give you three terms when expanded - that would have caught this error because your expansion only had two.