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A particle $P$ starts from rest at a fixed origin $O$. The acceleration of $P$ at time $t$ seconds (where $t\geq0$) is ($6t^2\mathbf{i} + (8-4t^3)\mathbf{j})\textrm{ms}^{-2}$. Find a. the velocity of $P$ when $t=2$ b.The position vector of $P$ when $t=4$ a: \begin{align} \mathbf{a} &= 6t^2\mathbf{i} + (8-4t^3)\mathbf{j}\\ \mathbf{v} &= 2t^3\mathbf{i} + (8t -t^4)\mathbf{j} + C\\ C &= 0\\ t &= 2\\ \mathbf{v} &= 16\mathbf{i} \end{align} b: \begin{align} \mathbf{v} &= 2t^3\mathbf{i} + (8t -t^4)\mathbf{j} \\ \mathbf{r} &= \frac{1}{2}t^4\mathbf{i} + \left(4t^2 - \frac{t^5}{5}\right)\mathbf{j} + K\\ K&=0\\ t&=4\\ \mathbf{r}&=128\mathbf{i} - 140\frac{4}{5}\mathbf{j} \end{align}
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Thu, 29 Mar 2018 12:05 GMT