An object of mass 3,kg is at rest. If a force | vedclass

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(A) Given mass $m = 3\,kg$ and force $\vec{F} = (6t^2\hat{i} + 4t\hat{j})\,N$.Using Newton's second law,$\vec{a} = \frac{\vec{F}}{m} = \frac{6t^2\hat{

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$18\hat{i} + 6\hat{j}$

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(A) Given mass $m = 3\,kg$ and force $\vec{F} = (6t^2\hat{i} + 4t\hat{j})\,N$.Using Newton's second law,$\vec{a} = \frac{\vec{F}}{m} = \frac{6t^2\hat{i} + 4t\hat{j}}{3} = (2t^2\hat{i} + \frac{4}{3}t\hat{j})\,m/s^2$.Since the object starts from rest,$\vec{v}(0) = 0$. The velocity $\vec{v}$ at time $t$ is given by $\vec{v} = \int_{0}^{t} \vec{a} dt$.$\vec{v} = \int_{0}^{3} (2t^2\hat{i} + \frac{4}{3}t\hat{j}) dt$.$\vec{v} = [\frac{2t^3}{3}\hat{i} + \frac{4t^2}{6}\hat{j}]_{0}^{3}$.$\vec{v} = [\frac{2(3)^3}{3}\hat{i} + \frac{4(3)^2}{6}\hat{j}] = [\frac{54}{3}\hat{i} + \frac{36}{6}\hat{j}] = 18\hat{i} + 6\hat{j}\,m/s$.

An object of mass $3\,kg$ is at rest. If a force $\vec{F} = (6t^2\hat{i} + 4t\hat{j})\,N$ is applied on the object,then the velocity of the object at $t = 3\,s$ will be

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