Question

Starting from the origin at time $t=0$, with initial velocity $5 \hat{ j } \,ms ^{-1},$ a particle moves in the $x - y$ plane with a constant acceleration of $(10 \hat{ i }+4 \hat{ j }) ms ^{-2} .$ At time $t$, its coordinates are (20 $\left. m , y _{0} m \right)$. The values of $t$ and $y _{0}$, are respectively

• A. $4 \,s$ and $52\, m$
• B. $2\, s$ and $24\, m$
• C. $2\, s$ and $18\, m$
• D. $5\, s$ and $25\, m$

Answer 1

Answer: (C)

Given $\vec{ u }=5 \hat{ j } m / s , \vec{ a }=10 \hat{ i }+4 \hat{ j },$ final coordinate
$\left(20, y_{0}\right)$ in time $t$
$S_{x}=4_{x} t+\frac{1}{2} a_{x} t^{2}$
$20-0=0+\frac{1}{2} \times 10 \times t^{2}$
$t=2 sec$
$S_{y}=u_{y} \times t+\frac{1}{2} a_{y} t^{2}$
$y _{0}=5 \times 2+\frac{1}{2} 4 \times 2^{2}=18 m$
$2 \sec$ and $18 m$