Question

The position co-ordinates of a particle moving in a 3-D coordinates system is given by
x = a cosωt
y = a sinωt
and z = aωt
The speed of the particle is:
(A) √(2) aω (B) aω
(C) √(3) aω (D) 2aω

Answer 1

The speed of the particle is:

(A)√(2) aω

This can be calculated as follows:

• As per the question,

        x = a cosωt

        y = a sinωt

        z = aωt

• Now,

        Velocity in x-direction (Vx) = −aωsinωt

        Velocity in y-direction (Vy) = aωcosωt

        Velocity in z-direction (Vz) = aω

• Resultant velocity (V) = √( Vx²+Vy²​+Vz²​)

​                                             = √[ (−aωsinωt)² + (aωcosωt)² + (aω)² ]

                                            = √(2a²ω²)

                                            = √(2) aω

Therefore, the speed of the particle moving in a 3-D coordinates system is √(2) aω