The velocity of a particle is given by $v = 12 + 3 (t + 7 t^{2})$ . What is the acceleration of the particle?

3 + 21 t

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3 + 42 t

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42 t

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4 t

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Solution

The correct option is B $3 + 42 t$
Given: $v = 12 + 3 (t + 7 t^{2})$

$\Rightarrow v = 12 + 3 t + 21 t^{2}$

Now, we know that

$a = \frac{d v}{d t}$

So,
$a = \frac{d (12 + 3 t + 21 t^{2})}{d t} = 3 + 42 t$ .

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