A student obtains the following values of two variables $r$ and $Y$.

r / cm	t / s
6.2	4.6
12.0	6.0

The first value of $r$ has an uncertainty of $\pm 0.2 \mathrm{cm}$, which is much greater than the percentage uncertainty in $t$. Do the results show that $t^2$ is proportional to $r$ ?

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(a) $A+B$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(b) $B-A$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(c) $C\times D$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(d) $\frac{B}{D}$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(e) $A^2$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(f) $2\times A$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(g) The square root of $(A\times B)$. (Recall that the square root of $x$ can be written as $x^{1/3}$.)