Question

The formula to determine energy is E=1/2mv^2
. What is the formula solved for v?

Answer 1

\(E=\Large \frac{1}{2mv^2}\)
You are solving for v in this equation, but this equation is solved for E. Do you have any ideas on where to begin?

Answer 2

No idea honestly. I just know the answer..

Answer 3

multiply times the inverse any fraction in your case 1/2 -> inverse = 2
divide over other variables , keep what you want
take the square root

neglect the negative root.

Answer 4

This is kinetic energy \[KE = \frac{ 1 }{ 2 }mv^2\]

Answer 5

\[\color{red}{2} \times KE =(\frac{ 1 }{ 2 }mv^2) \times \color{red}{2} \implies 2 KE = mv^2\] see how that works so far?

Answer 6

Yes. Multiply by the inversion to eliminate the 1/2

Answer 7

How can we get rid of the m on the right?

Answer 8

ummm... I would think Subtraction property?

Answer 9

Why, notice it's being multiplied by the v^2

Answer 10

What if we did this \[\color{red}{\frac{ 1 }{ m }} \times 2KE = (mv^2) \times \color{red}{\frac{ 1 }{ m }}\]

Answer 11

\[\implies \frac{ 2 KE }{ m } = v^2\] so we have this, then what?

Answer 12

then would need to eliminate the Coefficient and the exponent.??

Answer 13

We need to get rid of the exponent try this, \[x^2 = something \implies x = \sqrt{something}\]

Answer 14

hmmm.. so wait.. Relating to the \[v=\pm \sqrt{\frac{ 2KE }{ m }}\].. how do you eliminate the K?

Answer 15

The KE just means kinetic energy, I replaced the E with KE to show the difference as we usually use E for total energy you can leave it as E however :)

Answer 16

ohhhh ok. so the answer is indefinitely \[v=\pm \sqrt{\frac{ 2E }{ m }}\]

Answer 17

Yes, that's fine :)