The velocity of a body of mass 2 , kg as a fu | vedclass

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Question

(A) Given mass $m = 2 \, kg$ and velocity $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$.At $t = 2 \, s$,the velocity is:$\vec{v}(2) = 2(2) \hat{i} + (2)^2 \

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Momentum = $(8 \hat{i} + 8 \hat{j}) \, kg \cdot m/s$,Force = $(4 \hat{i} + 8 \hat{j}) \, N$

Vedclass · Answer

(A) Given mass $m = 2 \, kg$ and velocity $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$.At $t = 2 \, s$,the velocity is:$\vec{v}(2) = 2(2) \hat{i} + (2)^2 \hat{j} = 4 \hat{i} + 4 \hat{j} \, m/s$.Momentum $\vec{p} = m\vec{v} = 2(4 \hat{i} + 4 \hat{j}) = (8 \hat{i} + 8 \hat{j}) \, kg \cdot m/s$.Acceleration $\vec{a} = \frac{d\vec{v}}{dt} = \frac{d}{dt}(2t \hat{i} + t^2 \hat{j}) = 2 \hat{i} + 2t \hat{j}$.At $t = 2 \, s$,acceleration is:$\vec{a}(2) = 2 \hat{i} + 2(2) \hat{j} = 2 \hat{i} + 4 \hat{j} \, m/s^2$.Force $\vec{F} = m\vec{a} = 2(2 \hat{i} + 4 \hat{j}) = (4 \hat{i} + 8 \hat{j}) \, N$.

The velocity of a body of mass $2 \, kg$ as a function of $t$ is given by $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$. Find the momentum and the force acting on it at time $t = 2 \, s$.

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