Question

It's timed plzzz help!!!

Answer 1

`D.v= \± \sqrt{(2E)/(m)}`

Explanation:

`We\ are\ given\ that,\\Kinetic\ Energy\ possessed\ by\ an\ object=(1)/(2)mv^2\\Hence,\\E_k=(1)/(2)mv^2\\2E=2*(1)/(2)mv^2 [Multiplying\ both\ the\ sides\ with\ 2]\\2E=mv^2\\(2E)/(m)=(mv^2)/(m)[Dividing\ both\ the\ sides\ by\ m]\\(2E)/(m)=v^2\\Now,\\As\ v\ could\ be\ positive\ or\ negative\ but\ its\ square(v^2)\ would\ always\ be\ positive.\\`

`(\± v)^2= v^2\\Hence,\\(2E)/(m)= (\±v)^2 \\\sqrt{(2E)/(m)} = \±v\\Or,\\ v= \± \sqrt{(2E)/(m)}`

Answer 2

Last Choice / D

Explanation:

you want to isolate v!

E = 1/2 m v^2

multiply both sides by 2

2E = mv^2

divide both sides by m

2E/m = v^2

square root both sides

v = ±
`√(2E/m)`

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