If $r = t^{2} i - t j + (2 t + 1) k$ , find $| d r / d t |$ .

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Solution

$r = t^{2}^i - t^j + (2 t + 1)^k$

$\frac{d r}{d t} = (\frac{d}{d t} t^{2})^i - (\frac{d}{d t} t)^j + (\frac{d}{d t} (2 t + 1))^k$

$= 2 t^i -^j + 2^k$

$| \frac{d r}{d t} | = \sqrt{(2 t)^{2} + (- 1)^{2} + (2)^{2}}$

$= \sqrt{4 t^{2} + 5}$

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