What would you like to understand?

For addition and subtraction, the absolute uncertainties of the inputs combine in quadrature. The plus or minus signs in the formula do not matter because they are squared in the propagation equation, resulting in the same rule for both operations.

Conditions: The derived quantity is a sum or difference of two measured variables ($z = \pm x \pm y$).; The variables $x$ and $y$ are independent measured quantities.

For addition and subtraction, the absolute uncertainties of the inputs combine in quadrature. The plus or minus signs in the formula do not matter because they are squared in the propagation equation, resulting in the same rule for both operations.

Conditions: The derived quantity is a sum or difference of two measured variables ($z = \pm x \pm y$).; The variables $x$ and $y$ are independent measured quantities.

When both mass and velocity are measured, the uncertainty in kinetic energy is found by adding the two uncertainty sources in quadrature. You compute the partial derivative of kinetic energy with respect to each variable, multiply each derivative by the corresponding absolute uncertainty, square those terms, sum them, and take the square root.

Conditions: The kinetic energy formula is $K = \frac{1}{2}mv^2$.; Both mass $m$ and velocity $v$ carry independent absolute uncertainties $\delta m$ and $\delta v$.; The uncertainties are small enough for a first-order linear approximation.

When both mass and velocity are measured, the uncertainty in kinetic energy is found by adding the two uncertainty sources in quadrature. You compute the partial derivative of kinetic energy with respect to each variable, multiply each derivative by the corresponding absolute uncertainty, square those terms, sum them, and take the square root.

Conditions: The kinetic energy formula is $K = \frac{1}{2}mv^2$.; Both mass $m$ and velocity $v$ carry independent absolute uncertainties $\delta m$ and $\delta v$.; The uncertainties are small enough for a first-order linear approximation.