Q.

The position vector of a particle R as a function of time is given by:
R=4sin(2πt)i^+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?

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a

Acceleration vectors is along - R

b

Magnitude of the velocity of particle is 8 meter/ second.

c

Path of the particle is a circle of radius 4 meter

d

Magnitude of acceleration vector is v2R where v is the velocity of particle

answer is D.

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Detailed Solution

R=4sin(2πt)i^+4cos(2πt)j^V=dRdt=8πcos2πti^8πsin2πtj^
|V|=8π2 m/sec;  magnitude of the velocity  is not equal to 8m/sec.

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