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The following formula gives an object's kinetic energy
K, where
m is the object's mass and
v is the object's velocity.

K=(1)/(2)mv^(2)
Rearrange the formula to highlight mass.

m=

The following formula gives an object's kinetic energy $K$ , where $m$ is the object's mass and $v$ is the object's velocity. $\newline$ $K=\frac{1}{2} m v^{2}$ $\newline$ Rearrange the formula to highlight mass. $\newline$ $m=$

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. The following formula gives an object's kinetic energy

K

, where

m

is the object's mass and

v

is the object's velocity.

\newline

K=\frac{1}{2} m v^{2}

\newline

Rearrange the formula to highlight mass.

\newline

m=

Write formula for kinetic energy: Write down the original formula for kinetic energy. $\newline$ $K = \frac{1}{2}mv^2$
Isolate mass term: Isolate the term with mass $m$ on one side of the equation. $\newline$ To do this, we need to get rid of the fraction and the velocity squared term that are multiplied by the mass. $\newline$ First, multiply both sides of the equation by $2$ to eliminate the fraction. $\newline$ $2K = mv^2$
Eliminate fraction and velocity squared term: Now, divide both sides of the equation by $v^2$ to isolate $m$ . $\newline$ $(2K) / v^2 = m$
Multiply both sides by $2$ : Check the rearranged formula to ensure it is correctly solved for mass $m$ . The formula now reads $m = \frac{2K}{v^2}$ , which correctly expresses mass in terms of kinetic energy $K$ and velocity $v$ .

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