Question

A particle moves in XY plane according to the law $x$ = $asin\left(t\right)$ and $y$ = $a(1-cos(t\left)\right)$ where a is constant. The particle traces :

• A. a parabola
• B. a straight line equallyinclined to x and y axes
• C. a circle
• D. a distance proportional to time.

Answer 1

The correct option is A a parabola

$x=a\sin t$

$y=a(1-\cos t)$

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

The particle is under the action and two components

$V^2=(a\cos t{)}^2+(a\sin t{)}^2=a^2({\sin }^{2}t+{\cos }^{2}t)$

$V=a$ constant.

Hence the particle trace is (A) parabola.