The phase difference between the instantaneous velocity and acceleration of a particle

The Phase Difference Between The Instantaneous Velocity And Acceleration Of Physics QuestionThe Phase Difference Between The Instantaneous Velocity And Acceleration Of Physics Question

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

Options

(a) π
(b) 0.707π
(c) zero
(d) 0.5π

Correct Answer:

0.5π

Explanation:

Let y = A sin ωt
vinst = dy/ dt = Aω cos ωt
vinst = Aω² sin (ωt + π/2)
Acceleration = – Aω² sin ωt = Aω²sin (π + ωt)
ɸ = π/2 = 0.5 π.

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