A body starts from the origin and moves along the X-axis such that the velocit

Discussion Forum : Motion In One Dimension

Question -

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4 t^{3} - 2 t)$ , where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin

Options:

A .

28 m / s^{2}

B .

22 m / s^{2}

C .

12 m / s^{2}

D .

10 m / s^{2}

Answer: Option B
:
B

Given v = $4 t^{3} - 2 t$ .

$∴ a = \frac{d v}{d t} = 12 t^{2} - 2$

and $x = \int v d t = \int (4 t^{3} - 2 t) d t = t^{4} - t^{2}$

When particle is at 2m from the origin, we have

$t^{4} - t^{2} = 2$

$\Rightarrow t^{4} - t^{2} - 2 = 0$

$(t^{2} - 2) (t^{2} + 1) = 0 \Rightarrow t = \sqrt{2}$ sec (only possible physical root)

Acceleration at $t = \sqrt{2}$ sec given by,

$a = 12 t^{2} - 2 = 12 \times 2 - 2 = 22 m / s^{2}$

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