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Derivative from First Principle

The position ...

Question

The position $x$ of a particle varies with time $t$ according to the relation $x = t^{3} + 3 t^{2} + 2 t$ . Find velocity and acceleration as functions of time.

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Solution

$x = t^{3} + 3 t^{2} + 2 t \Rightarrow v = \frac{d x}{d t} = 3 t^{2} + 6 t + 2$
$\Rightarrow a = \frac{d v}{d t} = 6 t + 6$

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