Question

If t is 04.00s, then what is the percentage uncertainty in t^2?

Answer 1

That depends upon the uncertainty in t. The relative, or percentage, uncertainty, is twice as much for t^2 as it is for t.

Here is why:
ln(t^2) = 2 ln t
d(t^2)/t^2 = 2 dt/t

Since three significant figures are being quoted for t, presumably the relative uncertainty in t is +/- 0.005/4 = 0.00125 or 0.125%

The uncertainty in t^2 is then 0.25%