Question

A particle has a constant acceleration of a=\vec{a}= (6.0 m/s2)i^+(4.0 m/s2)j^\left(6.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{i}+\left(4.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{j}. At time t=0t=0, the velocity is zero and the position vector is r0=(10 m)i^\vec{r}_0=(10 \mathrm{~m}) \hat{i}.

(b)(b) Find the equation of the particle's path in the xyx y plane and sketch the path.

Solution

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(b)(b) In this part, we need to find an expression of the particle's path in the xyx-y plane and a sketch of the path. The following expression is given from the part (a)(a):

r=[(10.0 m)+(3.0 ms2)t2]i^+[(2.0 ms2)t2]j^\vec{r}=\left[\left(10.0\mathrm{~m}\right)+\left(3.0\mathrm{~\dfrac{m}{s^2}}\right)t^2\right]\hat{i}+\left[\left(2.0\mathrm{~\dfrac{m}{s^2}}\right)t^2\right]\hat{j}

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