Lets say you have:
KE = 1/2mv^2 and then you double KE. The velocity increases by a factor of square root 2. Can someone show the algebraic steps to this. Thank you
I would think about it like this:
You can't increase mass, so you must increase velocity, right? We want the total KE doubled, so:
KE = (1/2)*m*(v)^2
needs to become
KE = 2*(1/2)*m*(v)^2
This means we need to put something into the parentheses that contain "v" that, when squared (and thus pulled out from the parentheses under the exponent), will give us a coefficient of 2. What can we put in as a coefficient of "v" that will be squared to yield 2? The square root of 2 of course.