Question

A particle starts from the origin at $t =0 \,s$ with a velocity of $10\, \hat{ j }\, ms ^{-1}$ and move in the $x - y$ plane with a constant acceleration of $(8 \hat{ j }+2 \hat{ j }) ms ^{-2}$. At an instant when the $x$-coordinate of the particle is $16\, m , y$-coordinate of the particle is:

• A. 16 m
• B. 28 m
• C. 36 m
• D. 24 m

Answer 1

Answer: (D)

$\vec{ r }=\vec{ u } t +\frac{1}{2} \vec{ a } t ^{2}$
$x \hat{ i }+ y \hat{ j }=10 t \hat{ j }+\frac{1}{2}(8 \hat{ i }+2 \hat{ j }) t ^{2}$
$x \hat{ i }+ y \hat{ j }=10 t \hat{ j }+(4 \hat{ i }+\hat{ j }) t ^{2}$
$16 \hat{ i }+ yj =10 t \hat{ j }+4 t ^{2} \hat{ i }+ t ^{2} \hat{ j }$
$16 \hat{ i }+\hat{ j }=4 t ^{2} \hat{ i }+\left(10 t + t ^{2}\right) \hat{ j }$
$4 t ^{2}=16$
$t =4 s$
$y =10 t + t ^{2}$
$=20+4=24 \,m .$