The velocity of a particle is given as The magnitude of acceleration at point (1,2,4) is

Question

The velocity of a particle is given as $\vec{v} = - x \hat{i} + 2 y \hat{j} - z \hat{k} m / s .$ The magnitude of acceleration at point (1,2,4) is ______ $m / s^{2}$ . [2026]

Smart Achievers · Accepted Answer

(2)

$\vec{v} = - x \hat{i} + 2 y \hat{j} - z \hat{k}$

$\frac{\partial \vec{v}}{\partial t} = - \frac{\partial x}{\partial t} \hat{i} + 2 \frac{\partial y}{\partial t} \hat{j} - \frac{\partial z}{\partial t} \hat{k}$

$\vec{a} = - v_{x} \hat{i} + 2 v_{y} \hat{j} - v_{z} \hat{k}$

$\vec{a} = x \hat{i} + 4 y \hat{j} + z \hat{k}$

$∴$ $\vec{a} at (1, 2, 4) = \hat{i} + 8 \hat{j} + 4 \hat{k}$

$| \vec{a} |$ $= \sqrt{1 + 64 + 16} = 9$

$∴$ $| \vec{a} |$ $= 9 {m/s}^{2}$

Solution

Q.
The velocity of a particle is given as $\vec{v} = - x \hat{i} + 2 y \hat{j} - z \hat{k} m / s .$ The magnitude of acceleration at point (1,2,4) is ______ $m / s^{2}$ . [2026]

1 $\sqrt{6}$

2 $9$

3 $\sqrt{33}$

4 $0$

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