Question

unit 1 test: solving equations
started: oct 3 at 8:43am
quiz instructions
question 1
solve for v: $ke = \frac{1}{2}mv^{2}$
$v = \frac{1}{2}kem$
$v = \sqrt{\frac{2ke}{m}}$
$v = \sqrt{\frac{ke}{2m}}$
$v = \frac{(2ke)^{3}}{m}$

Explanation:

Step1: Isolate $v^{2}$

Multiply both sides by 2 and divide by $m$: $v^{2}=\frac{2KE}{m}$

Step2: Solve for $v$

Take square - root of both sides: $v = \pm\sqrt{\frac{2KE}{m}}$, considering the physical context (usually speed is non - negative in basic kinetic energy formula applications, but mathematically we have two solutions). Ignoring the negative solution for speed in a basic sense, we get $v=\sqrt{\frac{2KE}{m}}$

Answer:

$v=\sqrt{\frac{2KE}{m}}$