Solve for t in the equation K = m sqrt((t-p)/(m))

Question

ScanSolve AI Tutor · Accepted Answer

Your steps are mostly correct, but there is an error in one line that leads to an incorrect final answer.

Here's a breakdown of the correct steps:

Given the equation:

K = m \sqrt{\frac{t-p}{m}}

Divide both sides by $m$ .
$\frac{K}{m} = \sqrt{\frac{t-p}{m}}$
Square both sides to eliminate the square root.
$\left(\frac{K}{m}\right)^2 = \left(\sqrt{\frac{t-p}{m}}\right)^2$ $\frac{K^2}{m^2} = \frac{t-p}{m}$
Multiply both sides by $m^2$ to clear the denominators.
Your step $K^2 = m^2 t - m^2 p$ is incorrect. When you multiply $\frac{t-p}{m}$ by $m^2$ , one $m$ in the numerator cancels with the $m$ in the denominator.
$m^2 \cdot \frac{K^2}{m^2} = m^2 \cdot \frac{t-p}{m}$ $K^2 = m(t-p)$
Distribute $m$ on the right side.
$K^2 = mt - mp$
Add $mp$ to both sides to isolate the term containing $t$ .
$K^2 + mp = mt$
Divide both sides by $m$ to solve for $t$ .
$\frac{K^2 + mp}{m} = t$
The correct final answer is:
$t = \frac{K^2 + mp}{m}$

Answer