Question

the equation $k=\frac{1}{2}mv^{2}$ shows that the kinetic energy $k$ of an object depends on the mass $m$ of the object and the square of the velocity $v$ of the object. which equation correctly expresses the mass of the object in terms of its velocity and kinetic energy? a $m = 2kv^{2}$ b $m=\frac{1}{2}kv^{2}$ c $m=\frac{2k}{v^{2}}$ d $m=\frac{k}{2v^{2}}$

Explanation:

Step1: Isolate the mass variable.

Given $k=\frac{1}{2}mv^{2}$, multiply both sides by 2 to get $2k = mv^{2}$.

Step2: Solve for m.

Divide both sides of $2k = mv^{2}$ by $v^{2}$ (assuming $v
eq0$), we have $m=\frac{2k}{v^{2}}$.

Answer:

C. $m=\frac{2k}{v^{2}}$