Question

An object moves in x – y plane. Equations for displacement in x and y direction are x = 3sin2t and y = 3cos2t Speed of the particle is 

(A) zero 

(B) constant and nonzero 

(C) increasing with time t 

(D) decreasing with time t

Answer 1

Correct option: (B) constant and nonzero

Explanation:

x = 3 sin 2t ∴ Vx = (dx / dt) = 6 cos 2t

y = 3 cos 2t   Vy = (dy / dx) = 6(– sin 2t)

hence speed = V = √(Vx² + Vy²) = √(6² cos² 2t + 6² sin² 2t)

= 6(1) = 6 m/s i.e. nonzero & constant