The displacement of a particle is given by $(x = 2 t^{2} + t + 5)$ m. Find its acceleration at t = 2 s.

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Solution

$x = 2 t^{2} + t + 5$
Velocity of the particle, $v = \frac{d x}{d t}$
$= \frac{d (2 t^{2} + t + 5)}{d t}$
$\Rightarrow v = 4 t + 1$
Acceleration of particle, $a = \frac{d v}{d t}$
$= \frac{d (4 t + 1)}{d t}$
$\Rightarrow a = 4 m / s^{2}$
The acceleration of the particle is independent of time.
So, acceleration of the particle at t = 2 s is $4 m / s^{2}$ .

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