The position vector of a particle R → as a function of time is given by: R → = 4 sin ⁡ 2 π t i ^ + 4 c o s ⁡…

The position vector of a particle R→ as a function of time is given by:
R→=4sin⁡2πti^+4cos⁡(2πt)j^
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. Magnitude of acceleration vector is v2R , where v is the velocity of particle
  2. Magnitude of the velocity of particle is 8 meter/second
  3. Patch of the particle is a circle of radius 4 meter
  4. Acceleration vector is along -R→

Solution

x=4 sin2πt
y=4cos⁡(2πt) 

Squaring and adding

x2+y2=4sin2πt2+4cos2πt2

x2+y2=16

This means the particle is moving in a circle
V=rω=2π4=8π

Asked in: NEET 2015 (Phase 2)

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