An object of mass 2 , kg at rest at the origi | vedclass

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(C) Given: Mass $m = 2 \, kg$,initial velocity $\vec{u} = 0$,force $\vec{F} = (3t^2 \hat{i} + 4 \hat{j}) \, N$.According to Newton's second law,$\vec{

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$(4 \hat{i} + 4 \hat{j})$

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(C) Given: Mass $m = 2 \, kg$,initial velocity $\vec{u} = 0$,force $\vec{F} = (3t^2 \hat{i} + 4 \hat{j}) \, N$.According to Newton's second law,$\vec{F} = m \vec{a} = m \frac{d\vec{v}}{dt}$.Therefore,$d\vec{v} = \frac{\vec{F}}{m} dt$.Integrating both sides from $t = 0$ to $t = 2 \, s$:$\int_{0}^{\vec{v}} d\vec{v} = \int_{0}^{2} \frac{3t^2 \hat{i} + 4 \hat{j}}{2} dt$.$\vec{v} = \frac{1}{2} \left[ \int_{0}^{2} 3t^2 dt \hat{i} + \int_{0}^{2} 4 dt \hat{j} \right]$.$\vec{v} = \frac{1}{2} \left[ (t^3)_{0}^{2} \hat{i} + (4t)_{0}^{2} \hat{j} \right]$.$\vec{v} = \frac{1}{2} [ (8 - 0) \hat{i} + (8 - 0) \hat{j} ]$.$\vec{v} = \frac{1}{2} [ 8 \hat{i} + 8 \hat{j} ] = 4 \hat{i} + 4 \hat{j} \, m/s$.

An object of mass $2 \, kg$ at rest at the origin starts moving under the action of a force $\vec{F} = (3t^2 \hat{i} + 4 \hat{j}) \, N$. The velocity of the object at $t = 2 \, s$ will be ............. $m/s$.

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