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The \( \mathrm{x} \) and \( \mathrm{y} \) coordinates of a particle moving in a plane are given by \( x(t)=a \cos (\mathrm{pt}) \) and
\( \mathrm{P} \) \( \mathrm{y}(\mathrm{t})=\mathrm{b} \sin (\mathrm{pt}) \) where \( \mathrm{a}, \mathrm{b}(\mathrm{a}) \) and \( \mathrm{p} \) are positive constants of appropriate dimensions and t is time. Then,
(1) the path of the particle is an ellipse.
- (2) velocity and acceleration of the particle are perpendicular to each other at \( \mathrm{t}=\pi / 2 \mathrm{p} \).
(3) acceleration of the particle is always directed towards a fixed point.
(4) All of these
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