The position vector of a particle R as a function of time is given by… | NEET 2015 (AIPMT)

Q16NEET 2015 · AIPMTMedium

Motion in a Plane (2-D Kinematics)

The position vector of a particle $\vec{R}$ as a function of time is given by $\vec{R}$ = 4sin(2 $\pi t)\hat{i}$ + 4cos(2 $\pi t)\hat{j}$ . Where R is in meters, t is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

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Answer: (a)

$|\vec R| = 4$ m always, so the path is a circle of radius 4 m: (b) true.
$\vec v = 8\pi\cos(2\pi t)\hat i - 8\pi\sin(2\pi t)\hat j$ , so $|\vec v| = 8\pi$ m/s, not 8 m/s: (a) wrong.
$\vec a = -4\pi^2\vec R$ , along $-\vec R$ with magnitude $\frac{v^2}{R}$ : (c), (d) true.
So the wrong statement is (a).

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