Solve the Problem $K$ Of an Object with Mass $m$ And Velocity $v$

Multiple Choice

Solve the problem.
-The kinetic energy $K$ of an object with mass $m$ and velocity $v$ is $K = \frac { 1 } { 2 } m v ^ { 2 }$ . How is $\mathrm { dm } / \mathrm { dt }$ related to $\mathrm { dv } / \mathrm { dt }$ if $K$ is constant?

A) $\frac { d v } { d t } = - \frac { 2 m } { v } \frac { d m } { d t }$
B) $\frac { d m } { d t } = \frac { m } { v } \frac { d v } { d t }$
C) $\frac { d m } { d t } = - 2 m v ^ { 3 } \frac { d v } { d t }$
D) $\frac { \mathrm { dm } } { \mathrm { dt } } = - \frac { 2 \mathrm {~m} } { \mathrm { v } } \frac { \mathrm { dv } } { \mathrm { dt } }$