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Derivative from First Principle

The displacem...

Question

The displacement of a particle along the x-axis is given by $x = 3 + 8 t + 7 t^{2}$ . Obtain its velocity and acceleration at $t = 2 s$ .

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Solution

$D i s t a n c e x = 3 + 8 t + 7 t^{2}, V e l o c i t y v = \frac{d x}{d t} = 8 + 14 t$
$v_{t = 2 s} = 8 + 14 \times 2 = 36 m s^{- 1}, a = \frac{d v}{d t} = 14 m s^{- 2}$

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