At time t =0 a particle starts travelling from a height 7,hat{z} cm in a plane keeping z coordinate

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3-2.Motion in Plane

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At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.

A$-30\,\hat y$

B$30\,\hat y$

C$3 \hat x+15 \hat y$

D$3 \hat x+15 \hat y+7 \hat{z}$

(JEE MAIN-2022)

Solution

$\overrightarrow{ r }=3 t \hat{ i }+5 t ^{3} \hat{ j }+7 k$
$\frac{ d ^{2} \overrightarrow{ r }}{ dt ^{2}}=30 t \hat{ j }$
At $t=1 \Rightarrow \frac{d^{2} \overrightarrow{r}}{{d t^{2}}}=30\,\hat{j}$

Standard 11

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At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.

Solution

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