Question

Starting from the origin at time $t=0$, with initial velocity $5\hat{j}m{s}^{-1},$ a particle moves in the $x-y$ plane with a constant acceleration of $(10\hat{i}+4\hat{j})m{s}^{-2}.$ At time $t$, its coordinates are (20 $m,y_{0}m)$. The values of $t$ and $y_0$, are respectively

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

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 $t$
$S_x=4_{x}t+\frac{1}{2}{a}_x{t}^2$
$20-0=0+\frac{1}{2}\times 10\times t^2$
$t=2sec$
$S_y=u_y\times t+\frac{1}{2}{a}_y{t}^2$
$y_0=5\times 2+\frac{1}{2}4\times 2^2=18m$
$2\sec$ and $18m$