Question

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

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

Answer 1

The correct option is A $\text{2 s and 18 m}$

Given, $u=5\hat{j}{\text{ms}}^{-1}$
Acceleration, $a=10\hat{i}+4\hat{j}{\text{ms}}^{-1}$ and
Final position coordinates are $(20\text{m},y_0\text{m})$ at time $t$

$S_x=u_{x}t+\frac{1}{2}{a}_x{t}^2[\because u_x=0]$
$\Rightarrow 20=0+\frac{1}{2}\times 10\times t^2$
$\Rightarrow t=2\text{s}$
$S_y=u_{y}t+\frac{1}{2}{a}_y{t}^2$
$y_0=5\times 2+\frac{1}{2}\times 4\times 2^2=18\text{m}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.