Question

Find the distance $s$ traversed by the point during the small time interval from $0$ to $\tau$.

• A. $s=a\omega \tau$
• B. $s=2a\omega \tau$
• C. $s=4a\omega \tau$
• D. $s=6a\omega \tau$

Answer 1

The correct option is A $s=a\omega \tau$

$\overrightarrow{r}=asin\omega t\overrightarrow{i}+a(1-cos\omega t)\overrightarrow{j}|\overrightarrow{r}|=\sqrt{a^2{sin}^2\omega \tau +a^2{(1-cos\omega \tau )}^2}|\overrightarrow{r}|=a\sqrt{2-2cos\omega \tau }|\overrightarrow{r}|=a\sqrt{4si{n}^2\frac{\omega \tau }{2}}$
for very small time interval $\tau$
$sin\frac{\omega \tau }{2}=\frac{\omega \tau }{2}$
$|\overrightarrow{r}|=a\sqrt{4(\frac{\omega \tau }{2}{)}^2}$
$|\overrightarrow{r}|=a\omega \tau$