Question

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

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

Answer 1

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

Given: $\overrightarrow{u}=5\hat{j}\text{m/s}$
Acceleration, $\overrightarrow{a}=10\hat{i}+4\hat{j}$ and final coordinates $(20,y_0)$ in time $t$.

Using equation of motion along $\text{x-axis}$,

$x=u_{x}t+\frac{1}{2}{a}_x{t}^2$

$[\because u_x=0]$
$\Rightarrow 20=0+\frac{1}{2}\times 10\times t^2$

$\Rightarrow t=2\text{s}$

Using equation of motion along $\text{y-axis}$,

$y=u_y\times t+\frac{1}{2}{a}_y{t}^2$

$y=y_0=5\times 2+\frac{1}{2}\times 4\times 2^2=18\text{m}$

Hence, $\left(\text{A}\right)$ is the correct answer.