Kinematics 6 Question 4

4. In three dimensional system, the position coordinates of a particle (in motion) are given below

x=acosωty=asinωtz=aωt

The velocity of particle will be

(a) 2aω

(b) 2aw

(c) aω

(d) 3aω

(2019 Main, 09 Jan II)

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Answer:

Correct Answer: 4. (a)

Solution:

  1. Given that the position coordinates of a particle

x=acosωty=asinωtz=aωt

So, the position vector of the particle is

r^=xi^+yj^+zk^r^=acosωti^+asinωtj^+aωtk^r^=a[cosωti^+sinωtj^+ωtk^]

therefore, the velocity of the particle is

v^=drdt=d[a][cosωti^+sinωtj^+ωtk^]dtv^=aωsinωti^+aωcosωtj^+aωk^)

The magnitude of velocity is

|v|=vx2+vy2+vz2 or |v|=(aωsinωt)2+(aωcosωt)2+(aω)2=ωa(sinωt)2+(cosωt)2+(1)2=2ωa



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