question_answer 60)

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

Answer:

                  \[\upsilon (t)=2t\,\hat{i}~+\text{ }{{t}^{2}}\,\hat{j}\]                 \[a(t)=2\hat{i}+2t\,\hat{j}\]                 Momentum at \[t=2s,=mv\left( t \right){{|}_{t\text{ }=\text{ }2}}\]                 \[=2\times [4\hat{i}~+4\hat{j}]=(8\hat{i}~+8\hat{j})\text{ }kg\text{ }m{{s}^{1}}\]                 \[a(t){{|}_{t\text{ }=\text{ }2}}=(2\hat{i}+4\hat{j})\]                 \ \[F=ma\,{{(t)}_{t\text{ }=\text{ }2}}=(4~\hat{i}+8\hat{j})\text{ }N\]