Question

The position vector of a particle R as a function
of time is given by :-
R = 4 sin(2πt)i + 4 cos(2πt);
Where R is in meters, t is in seconds and i and
j denote unit vectors along x and y-directions,
respectively. Which one of the following statements
is wrong for the motion of particle ?
(1) Path of the particle is a circle of radius 4 meter
(2) Acceleration vectors is along -R
(3) Magnitude of acceleration vector is
where
v is the velocity of particle.
(4) Magnitude of the velocity of particle is
8 meter/second​

Answer 1

Answer:

Magnitude of the velocity vector is 35.54m/sec

Explanation:

velocity vector is =dr/dt =

$4 \times 2\pi \cos(2\pi \times t)i - 4 \times 2\pi \sin(2\pi \times t) j$

so, it's magnitude is

$\sqrt{(4 \times 2\pi)^{2} + (4 \times 2\pi)^{2} }$

=35.54m/sec