Question

A particle is moving on a curve given by $y=2\sin 2x$ ($x$ and $y$ are in metres). The x-component of velocity is always $2m/s$. If the particle starts from origin at $t=0$, then displacement in metres of the particle after $\frac{\pi }{2}s$ is (answer upto 2 decimal places)

Answer 1

$y=2\sin 2x,v_x=2m/s=\text{constant}$
At time $t=\frac{\pi }{2}s,x=2\times \frac{\pi }{2}=\pi m$
and, at same time instant.
$y=2\sin \pi =0$
$\overrightarrow{r}=\pi \hat{i}$
$\therefore \overrightarrow{d}={\overrightarrow{r}}_f-{\overrightarrow{r}}_i=\pi \hat{i}-0=\pi \hat{i}$
$d=\pi m$