Question

The $x$ and $y$ coordinates of a particle moving in a plane are given by $x(t) = a\ cos (pt)$ and $y(t) = b\ sin (pt)$ where $a, b$ $(<a$) and pare positive constants of appropriate dimensions and $t$ is time. Then, which of the following is not true?

• A. The path of the particle is an ellipse.
• B. Velocity and acceleration of the particle are perpendicular to each other at $t=\frac {\pi}{2p}$
• C. Acceleration of the particle is always directed towards a fixed point
• D. Distance travelled by the particle in time interval between $t = 0$ and $t = 2p$ is $a$.

Answer 1

Answer: (D)

Distance travelled by the particle in time interval between $t = 0$ and $t = 2p$ is $a$.

Answer 2

The correct option is (D): Distance travelled by the particle in time interval between $t = 0$ and $t = 2p$ is $a$.