At-time-t-the-force-acting-on-a-particle-P-of-mass-2kg-is-2ti-4j-N-P-is-initially-at-rest-at-the-point-with-position-vector-i-2j-Find-a-the-velocity-of-P-when-t-2-b-the-position-vector-w

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Question Number 38366 by Rio Mike last updated on 24/Jun/18

$$Attimet,theforceactingonaparticle$$$$Pofmass2kgis(2\mathit{t}\mathit{i}+4\mathit{j})N.P$$$$isinitiallyatrestatthepointwith$$$$positionvector(\mathit{i}+2\mathit{j}).$$$$Find:$$$$a)thevelocityofPwhent=2.$$$$b)thepositionvectorwhent=2.$$

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18

$$m\frac{d\overrightarrow{v}}{dt}=2t\overrightarrow{i}+4\overrightarrow{j}$$$$\frac{d\overrightarrow{v}}{dt}=t\overrightarrow{i}+2\overrightarrow{j}m=2kg$$$$d\overrightarrow{v}=t\overrightarrow{idt}+2\overrightarrow{jdt}$$$$\overrightarrow{v}=\frac{t^2}{2}\overrightarrow{i}+2\overrightarrow{jt}+c$$$$t=0\overrightarrow{v}=0c=0$$$$\overrightarrow{v}=\frac{t^2}{2}\overrightarrow{i}+2t\overrightarrow{j}$$$$\overrightarrow{v}=2\overrightarrow{i}+4\overrightarrow{j}whent=2$$$$\frac{d\overrightarrow{r}}{dt}=2\overrightarrow{i}+4\overrightarrow{j}$$$$\stackrel{}{r}=2t\overrightarrow{i}+4t\stackrel{\to r}{j}+c$$$$whent=0{\overrightarrow{r}}_0=\overrightarrow{i}+2\overrightarrow{j}$$$$\overrightarrow{r}=2t\overrightarrow{i}+4t\overrightarrow{j}+\overrightarrow{i}+2\overrightarrow{j}$$$$\overrightarrow{r}=\overrightarrow{i}(2t+1)+\overrightarrow{j}(4t+2)$$

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