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Derivative from First Principle

The displacem...

Question

The displacement of a particle is given by $y = (6 t^{2} + 3 t + 4) m$ , where $t$ is in seconds. Calculate the instantaneous speed of the particle.

12 t

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12 t + 3

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12 t + 4

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3 t + 3

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Solution

The correct option is D $12 t + 3$
Given the displacement of a particle is $y = (6 t^{2} + 3 t + 4) m$ .

Now, we know that
$v = \frac{d y}{d t}$

Hence,
$v = \frac{d (6 t^{2} + 3 t + 4)}{d t} = 12 t + 3$ .

So, at any instant(time) $t$ the instantaneous velocity of particle is given by $v = 12 t + 3$ .

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