1. Tardigrade
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  4. 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 hat x and hat y directions are defined as 3 t and 5 t 3 respectively. At t =1 s acceleration of the particle will be

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Q. 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 $\hat{ x }$ and $\hat{ y }$ directions are defined as $3 t$ and $5 t ^3$ respectively. At $t =1 s$ acceleration of the particle will be

JEE MainJEE Main 2022Motion in a Plane

Solution:

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