Answer
False
Work Step by Step
Given; $|r(t)|=1$ for all the value of $t$
$1$ can be written as;
$Sin^{2}t+cos^{2}t=1$
Let us suppose our function as $r(t)=(Sin(t^{2}),cos(t^{2}),0)$
Then
$r'(t)=(2tcost, -2t sint,0)$
$|r'(t)|=\sqrt{4t^{2}. cos^{2}t+4t^{2} sin^{2}t}$
$=2t(1)$
Thus, $|r'(t)|=2t$ which is not a constant.
Hence, the given statement is false.
