Question

E = v+½mv^2
make v the subject​

Answer 1

Step-by-step explanation:

Just complete the square:

[math]\qquad E=V+\frac{1}{2}MV^2[/math]

[math]\qquad 2ME=2MV+M^2V^2=(MV+1)^2-1[/math]

and solve for [math]V[/math]:

[math]\qquad V=\frac{1}{M}(\pm\sqrt{2ME+1}-1)[/math]

Allowing for +ve and -ve square roots there are two possible solutions, as you would expect since the given equation is a quadratic in [math]V[/math].