Question

A particle in xy plane is governed by x = A cos ω t, y = A (1 – sin ω t). A and ω are constants. What is the speed of the particle. 

(A) Aω t 

(B) Aω²t 

(C) Aω 

(D) A²ω sin (ωt / 2)

Answer 1

Correct option: (C) Aω

Explanation:

x = A cos ωt

∴ (dx / dt) = – Aω sin ωt       (1)

y = A (1 – sin ωt)

∴ (dy / dt) = A (– ω cos ωt)       (2)

from (1) & (2)

V_x = – Aω sin ωt

V_y = – Aω cos ωt

V = √(Vx² + Vy²) = √{(– Aω)² sin² ωt + (– Aω)² cos² ωt} = Aω.