Question

The equations of motion of a particle $P(x,y)$ on a plane are given by $x=4+r\cdot \cos t,y=6+r\cdot \sin t,$ where $t$ istime and $r$ is constant. Its velocity at time $t$ is

• A. $-\cot \left(t\right)$
• B. $-\tan \left(t\right)$
• C. $r$
• D. $r\cdot \tan \left(t\right)$

Answer 1

The correct option is C $r$

$x=4+r\cdot \cos t$ $y=6+r\sin t$

$\frac{dx}{dt}=-r\sin t$ $\frac{dy}{dt}=r\cos t$

$v_x=-r\sin t$ $V_y=r\cos t$

$|v|=\sqrt{v_{x^2}+v_{y^2}}=\sqrt{(-r\sin t{)}^2+(r\cos t{)}^2}$

$=\sqrt{r^2({\sin }^{2}t+{\cos }^{2}t}$

$|v|=r$.