Solution: (a)
Given the equation;
[tex]E=\frac{1}{2}mv^2[/tex]
Multiply both sides of the equation by 2;
[tex]\begin{gathered} 2\times E=2(\frac{1}{2})mv^2 \\ 2E=mv^2 \end{gathered}[/tex]
Divide both sides by the square of the velocity v;
[tex]\begin{gathered} \frac{2E}{v^2}=\frac{mv^2}{v^2} \\ m=\frac{2E}{v^2} \end{gathered}[/tex]
ANSWER:
[tex]m=\frac{2E}{v^2}[/tex]
(b) Given;
[tex]E=125,000J,v=24ms^{-1}[/tex]
We would substitute the value of the energy and the velocity into the formula for mass, we have;
[tex]\begin{gathered} m=\frac{2E}{v^2} \\ m=\frac{2(125000)}{24^2} \\ m=\frac{250000}{576} \\ m=434.03 \end{gathered}[/tex]
